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Courseware
This is a graduate-level introduction to mathematics of information theory. We will cover both classical and modern topics, including information entropy, lossless data compression, binary hypothesis testing, channel coding, and lossy data compression.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Information theory Information theory in mathematics
- Resource Type:
- Courseware
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e-book
Covers over 5,000 reports published by the National Academies Press for the National Academy of Sciences, National Academy of Engineering, Institute of Medicine and National Research Council in the US.
- Subjects:
- Physics, Chemistry, and Mathematics and Statistics
- Keywords:
- Physics Mathematics Chemistry
- Resource Type:
- e-book
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e-journal
OMICS International is an interactive open access journal for the communication of all scientific and medical research.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Mathematics
- Resource Type:
- e-journal
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Courseware
This course is the continuation of 18.785 Number Theory I. It begins with an analysis of the quadratic case of Class Field Theory via Hilbert symbols, in order to give a more hands-on introduction to the ideas of Class Field Theory. More advanced topics in number theory are discussed in this course, such as Galois cohomology, proofs of class field theory, modular forms and automorphic forms, Galois representations, and quadratic forms.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Galois cohomology Algebraic number theory Class field theory
- Resource Type:
- Courseware
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Courseware
This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Algebraic number theory
- Resource Type:
- Courseware
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Courseware
This graduate-level course is a computationally focused introduction to elliptic curves, with applications to number theory and cryptography.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Curves Elliptic
- Resource Type:
- Courseware
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Courseware
In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Fourier analysis Differential equations Partial
- Resource Type:
- Courseware
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Courseware
This course offers an in-depth the theoretical foundations for statistical methods that are useful in many applications. The goal is to understand the role of mathematics in the research and development of efficient statistical methods.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical statistics
- Resource Type:
- Courseware
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Courseware
This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Computational complexity
- Resource Type:
- Courseware
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Courseware
This course provides students with decision theory, estimation, confidence intervals, and hypothesis testing. It introduces large sample theory, asymptotic efficiency of estimates, exponential families, and sequential analysis.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical statistics
- Resource Type:
- Courseware
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Courseware
This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.
- Subjects:
- Philosophy and Mathematics and Statistics
- Keywords:
- Philosophy Ancient Mathematics -- Philosophy
- Resource Type:
- Courseware
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Courseware
Provides students with the basic tools for analyzing experimental data, properly interpreting statistical reports in the literature, and reasoning under uncertain situations. Topics organized around three key theories: Probability, statistical, and the linear model. Probability theory covers axioms of probability, discrete and continuous probability models, law of large numbers, and the Central Limit Theorem. Statistical theory covers estimation, likelihood theory, Bayesian methods, bootstrap and other Monte Carlo methods, as well as hypothesis testing, confidence intervals, elementary design of experiments principles and goodness-of-fit. The linear model theory covers the simple regression model and the analysis of variance. Places equal emphasis on theory, data analyses, and simulation studies.
- Subjects:
- Mathematics and Statistics and Biology
- Keywords:
- Statistics Cognitive science
- Resource Type:
- Courseware
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Courseware
This course provides a rigorous treatment of non-cooperative solution concepts in game theory, including rationalizability and Nash, sequential, and stable equilibria. It covers topics such as epistemic foundations, higher order beliefs, bargaining, repeated games, reputation, supermodular games, and global games. It also introduces cooperative solution concepts—Nash bargaining solution, core, Shapley value—and develops corresponding non-cooperative foundations.
- Subjects:
- Economics and Mathematics and Statistics
- Keywords:
- Game theory
- Resource Type:
- Courseware
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Courseware
This course is intended for both mathematics and biology undergrads with a basic mathematics background, and consists of an introduction to modeling biological problems using continuous ODE methods (rather than discrete methods as used in 113A). We describe the basic qualitative behavior of dynamical systems in the context of a simple population model and, as time allows, introduce other types of models such as chemical reactions inside the cell or excitable systems leading to oscillations and neuronal signals. Certain topics from linear algebra that are needed for this course are presented as well, so a linear algebra prerequisite is not necessary.
- Subjects:
- Mathematics and Statistics and Biology
- Keywords:
- Biology -- Mathematical models
- Resource Type:
- Courseware
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Courseware
Second introductory course covering basic principles of probability and statistical inference. Topics: Point estimation, interval estimating, and testing hypotheses, Bayesian approaches to inference.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities Mathematical statistics
- Resource Type:
- Courseware
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Courseware
Introductory course covering basic principles of probability and statistical inference. Topics covered in this course: Axiomatic definition of probability, random variables, probability distributions, expectation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities Mathematical statistics
- Resource Type:
- Courseware
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Courseware
After reviewing tools from probability, statistics, and elementary differential and partial differential equations, concepts such as hedging, arbitrage, Puts, Calls, the design of portfolios, the derivation and solution of the Blac-Scholes, and other equations are discussed.
- Subjects:
- Finance and Mathematics and Statistics
- Keywords:
- Business mathematics
- Resource Type:
- Courseware
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Courseware
This Pre-Calculus course is designed to prepare students for a calculus course. This course is taught so that students will acquire a solid foundation in algebra and trigonometry. The course concentrates on the various functions that are important to the study of the calculus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra
- Resource Type:
- Courseware
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Courseware
In this course, students will learn basic linear algebra necessary to understand the operations regarding derivatives of functions with more than one variable to investigate maximum and minimum values of those functions with economics applications in mind. Students will also see how to solve linear systems and then how to turn them into problems involving matrices, then learn some of the important properties of matrices. This course will focus on topics in linear algebra and multivariable differential calculus suitable for economic applications. Recorded Summer 2013
- Subjects:
- economic applications, matrices, Economics, and Mathematics and Statistics
- Keywords:
- Economics Mathematical
- Resource Type:
- Courseware
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Courseware
UCI Math 2A is the first quarter in Single-Variable Calculus and covers the following topics: Introduction to derivatives, calculation of derivatives of algebraic and trigonometric functions; applications including curve sketching, related rates, and optimization. Exponential and logarithm functions.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus
- Resource Type:
- Courseware
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Courseware
Math 2B is the second quarter of Single-Variable Calculus and covers the following topics: Definite integrals; the fundamental theorem of calculus. Applications of integration including finding areas and volumes. Techniques of integration. Infinite sequences and series. Parametric and polar equations.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus
- Resource Type:
- Courseware
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Courseware
Statistics is the science that turns data into information and information into knowledge. This class covers applied statistical methodology from an analysis-of-data viewpoint. Topics covered include frequency distributions; measures of location; mean, median, mode; measures of dispersion; variance; graphic presentation; elementary probability; populations and samples; sampling distributions; one sample univariate inference problems, and two sample problems; categorical data; regression and correlation; and analysis of variance. Use of computers in data analysis is also explored.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics
- Resource Type:
- Courseware
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Courseware
Mathematica and its applications to linear algebra, differential equations, and complex functions. Fourier series and Fourier transforms. Other topics in integral transforms.
- Subjects:
- Physics and Mathematics and Statistics
- Keywords:
- Physics Mathematical physics
- Resource Type:
- Courseware
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Courseware
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a real-life problem. You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program. If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way. This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve real-world problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical models
- Resource Type:
- Courseware
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Courseware
The lectures are at a beginning graduate level and assume only basic familiarity with Functional Analysis and Probability Theory. Topics covered include: Random variables in Banach spaces: Gaussian random variables, contraction principles, Kahane-Khintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γ-Radonifying operators, γ-boundedness, Brownian motion, Wiener stochastic integral. Stochastic evolution equations I: Linear stochastic evolution equations: existence and uniqueness, Hölder regularity. Stochastic integral in Banach spaces II: UMD spaces, decoupling inequalities, Itô stochastic integral. Stochastic evolution equations II: Nonlinear stochastic evolution equations: existence and uniqueness, Hölder regularity.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Stochastic partial differential equations Evolution equations
- Resource Type:
- Courseware
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Video
In this video we look at how to use statistical tables to calculate probabilities in a Poisson distribution. This includes an example of using the table for the probability density function to determine the probability the random variable is equal to particular value in a case where the average number of events per interval needs to be adjusted to match the units specified in the question and an example of using the table for the cumulative distribution function to determine the probability the random variable takes a value between two specified numbers.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Binomial distribution Probabilities Distribution (Probability theory)
- Resource Type:
- Video
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Video
In this video we look at how to use statistical tables to calculate probabilities in a Poisson distribution. This includes an example of using the table for the probability density function to determine the probability the random variable is equal to a particular value and an example of using the table for the cumulative distribution function to determine the probability the random variable is less than a certain value and an example determining the probability it is greater than or equal to a certain value.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities Poisson distribution Distribution (Probability theory)
- Resource Type:
- Video
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Video
In this video we look at how to use statistical tables to calculate probabilities in a Binomial distribution. This includes an example of using the table for the probability density function to determine the probability the random variable takes a particular value and an example of using the table for the cumulative distribution function to determine the probability the random variable is less than or equal to a certain value and an example determining the probability it is greater than or equal to a certain value.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities Poisson distribution Distribution (Probability theory)
- Resource Type:
- Video
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Video
In this video we look at how to decide for a given scenario (worded problem) if the distribution described is a Binomial distribution or Poisson distribution and whether its probability distribution function or its cumulative distribution function is required to calculate a specified probability.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Binomial distribution Probabilities Poisson distribution Distribution (Probability theory)
- Resource Type:
- Video
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Courseware
This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebras Linear
- Resource Type:
- Courseware
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Courseware
This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Mathematical optimization
- Resource Type:
- Courseware
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Courseware
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations
- Resource Type:
- Courseware
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Courseware
The course is taught using the textbook by T. Apostol, "Calculus" Vol. I Second Edition (1967) and the additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Mathematical analysis
- Resource Type:
- Courseware
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Video
Engineering Mathematics tutorial series covers aspects of applied mathematics including: multivariable calculus; vector field theory; differential equations; Laplace transforms and Fourier series.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Engineering mathematics
- Resource Type:
- Video
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Others
Euclid’s Elements was a collection of 13 books about geometry originally written circa 300 BC. Shortly after the advent of the printing press, many editions and translations have been created over the centuries. Byrne’s 1847 edition of the first six books stands out for its unique use of colorful illustrations to demonstrate proofs rather than using letters to label angles, edges, and shapes. His edition was one of the first books to be published with such detailed use of colors and combined with its detailed diagrams makes it an impressive feat of publishing for the times and it stands out even today as a work of art. This site is a reproduction of Byrne’s Euclid by Oliver Byrne from 1847 that pays tribute to the beautiful original design and includes enhancements such as interactive diagrams, cross references, and posters designed by Nicholas Rougeux.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Euclid's Elements Elements (Euclid) Geometry
- Resource Type:
- Others
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MOOC
This course teaches the R programming language in the context of statistical data and statistical analysis in the life sciences. We will learn the basics of statistical inference in order to understand and compute p-values and confidence intervals, all while analyzing data with R code. We provide R programming examples in a way that will help make the connection between concepts and implementation. Problem sets requiring R programming will be used to test understanding and ability to implement basic data analyses. We will use visualization techniques to explore new data sets and determine the most appropriate approach. We will describe robust statistical techniques as alternatives when data do not fit assumptions required by the standard approaches. By using R scripts to analyze data, you will learn the basics of conducting reproducible research. Given the diversity in educational background of our students we have divided the course materials into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. We start with simple calculations and descriptive statistics. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.
- Subjects:
- Statistics and Research Methods and Mathematics and Statistics
- Keywords:
- Life sciences -- Statistical methods Mathematical statistics -- Data processing R (Computer program language)
- Resource Type:
- MOOC
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MOOC
This course covers a wide variety of topics in machine learning and statistical modeling. While mathematical methods and theoretical aspects will be covered, the primary goal is to provide students with the tools and principles needed to solve the data science problems found in practice. This course also serves as a foundation on which more specialized courses and further independent study can build. This course was designed as part of the core curriculum for the Center for Data Science's Masters degree in Data Science. Other interested students who satisfy the prerequisites are welcome to take the class as well. Note that class is intended as a continuation of DS-GA-1001 Intro to Data Science, which covers some important, fundamental data science topics that may not be explicitly covered in this DS-GA class (e.g. data cleaning, cross-validation, and sampling bias).
- Course related:
- LGT6801 Guided Study in Logistics I
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Big data Data mining Machine learning Mathematical statistics -- Data processing
- Resource Type:
- MOOC
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Others
Math explained in easy language, plus puzzles, games, worksheets and an illustrated dictionary.
- Course related:
- AMA1110 Basic Mathematics I – Calculus and Probability & Statistics and AMA1120 Basic Mathematics II – Calculus and Linear Algebra
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics
- Resource Type:
- Others
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Video
Statistics, Machine Learning and Data Science can sometimes seem like very scary topics, but since each technique is really just a combination of small and simple steps, they are actually quite simple. My goal with StatQuest is to break down the major methodologies into easy to understand pieces. That said, I don't dumb down the material. Instead, I build up your understanding so that you are smarter.
- Course related:
- HTI34016 Introduction to Clinical Research
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Statistics Mathematical analysis Data mining Machine learning
- Resource Type:
- Video
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Others
Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration). All common integration techniques and even special functions are supported. The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions.
- Course related:
- AMA1120 Basic Mathematics II - Calculas and Linear Algebra
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Integral
- Resource Type:
- Others
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e-book
Collaborative Statistics was written by Barbara Illowsky and Susan Dean, faculty members at De Anza Collegein Cupertino, California. The textbook was developed over several years and has been used in regularand honors-level classroom settings and in distance learning classes. Courses using this textbook have beenarticulated by the University of California for transfer of credit. The textbook contains full materials forcourse offerings, including expository text, examples, labs, homework, and projects. A Teacher's Guide iscurrently available in print form and on the Connexions site at and supplemental course materials including additional problem sets and video lectures are available. The on-line text for each of these collections collections willmeet the Section 508 standards for accessibility. An on-line course based on the textbook was also developed by Illowsky and Dean. It has won an awardas the best on-line California community college course. The on-line course will be available at a later dateas a collection in Connexions, and each lesson in the on-line course will be linked to the on-line textbookchapter. The on-line course will include, in addition to expository text and examples, videos of courselectures in captioned and non-captioned format. The original preface to the book as written by professors Illowsky and Dean, now follows: This book is intended for introductory statistics courses being taken by students at two– and four–yearcolleges who are majoring in fields other than math or engineering. Intermediate algebra is the only prerequisite.The book focuses on applications of statistical knowledge rather than the theory behind it. Thetext is named Collaborative Statistics because students learn best by doing. In fact, they learn best byworking in small groups. The old saying “two heads are better than one” truly applies here. Our emphasis in this text is on four main concepts: thinking statistically incorporating technology working collaboratively writing thoughtfully These concepts are integral to our course. Students learn the best by actively participating, not by justwatching and listening. Teaching should be highly interactive. Students need to be thoroughly engagedin the learning process in order to make sense of statistical concepts. Collaborative Statistics providestechniques for students to write across the curriculum, to collaborate with their peers, to think statistically,and to incorporate technology. This book takes students step by step. The text is interactive. Therefore, students can immediately applywhat they read. Once students have completed the process of problem solving, they can tackle interestingand challenging problems relevant to today's world. The problems require the students to apply theirnewly found skills. In addition, technology (TI-83 graphing calculators are highlighted) is incorporatedthroughout the text and the problems, as well as in the special group activities and projects. The book alsocontains labs that use real data and practices that lead students step by step through the problem solvingprocess. At De Anza, along with hundreds of other colleges across the country, the college audience involves alarge number of ESL students as well as students from many disciplines. The ESL students, as well asthe non-ESL students, have been especially appreciative of this text. They find it extremely readable andunderstandable. Collaborative Statistics has been used in classes that range from 20 to 120 students, and inregular, honor, and distance learning classes.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
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e-book
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course. This text is, by far, the best elementary algebra textbook offered under a Creative Commons license. It is written in such a way as to maintain maximum flexibility and usability. A modular format was carefully integrated into the design. For example, certain topics, like functions, can be covered or omitted without compromising the overall flow of the text. An introduction of square roots in Chapter 1 is another example that allows for instructors wishing to include the quadratic formula early to do so. Topics such as these are carefully included to enhance the flexibility throughout. This textbook will effectively enable traditional or nontraditional approaches to elementary algebra. This, in addition to robust and diverse exercise sets, provides the base for an excellent individualized textbook instructors can use free of needless edition changes and excessive costs! A few other differences are highlighted below: Equivalent mathematical notation using standard text found on a keyboard A variety of applications and word problems included in most exercise sets Clearly enumerated steps found in context within carefully chosen examples Alternative methods and notation, modularly integrated, where appropriate Video examples available, in context, within the online version of the textbook Robust and diverse exercise sets with discussion board questions Key words and key takeaways summarizing each section This text employs an early-and-often approach to real-world applications, laying the foundation for students to translate problems described in words into mathematical equations. It also clearly lays out the steps required to build the skills needed to solve these equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. In addition to embedded video examples and other online learning resources, the importance of practice with pencil and paper is stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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e-book
This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solve equations, compute derivatives and integrals, multiply matrices and find determinants; and you have seen how these things can answer practical questions about the real world. In this setting, your primary goal in using mathematics has been to compute answers. But there is another approach to mathematics that is more theoretical than computational. In this approach, the primary goal is to understand mathematical structures, to prove mathematical statements, and even to invent or discover new mathematical theorems and theories. The mathematical techniques and procedures that you have learned and used up until now have their origins in this theoretical side of mathematics. For example, in computing the area under a curve, you use the fundamental theorem of calculus. It is because this theorem is true that your answer is correct. However, in your calculus class you were probably far more concerned with how that theorem could be applied than in understanding why it is true. But how do we know it is true? How can we convince ourselves or others of its validity? Questions of this nature belong to the theoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics. This text has been used in classes at:Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei, Christian Brothers High School, University of Texas Pan American, Schola Europaea, James Madison University, Heriot-Watt University, Prince of Songkla University, Queen Mary University of London, University of Nevada - Reno, University of Georgia - Athens, Saint Peter's University, California State University,Bogaziçi University, Pennsylvania State University, University of Notre Dame
- Subjects:
- Mathematics and Statistics
- Keywords:
- Proof theory Textbooks
- Resource Type:
- e-book
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e-book
College Algebra is an introductory text for a college algebra survey course. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The authors also offer a Precalculus version of this text, which has two extra chapters covering Trigonometry.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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e-book
A casual glance through the Table of Contents of most of the major publishers' College Algebra books reveals nearly isomorphic content in both order and depth. Our Table of Contents shows a different approach, one that might be labeled “Functions First.” To truly use The Rule of Four, that is, in order to discuss each new concept algebraically, graphically, numerically and verbally, it seems completely obvious to us that one would need to introduce functions first. (Take a moment and compare our ordering to the classic “equations first, then the Cartesian Plane and THEN functions” approach seen in most of the major players.) We then introduce a class of functions and discuss the equations, inequalities (with a heavy emphasis on sign diagrams) and applications which involve functions in that class. The material is presented at a level that definitely prepares a student for Calculus while giving them relevant Mathematics which can be used in other classes as well. Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. The answers to nearly all of the computational homework exercises are given in thetext and we have gone to great lengths to write some very thought provoking discussion questions whose answers are not given. One will notice that our exercise sets are much shorter than the traditional sets of nearly 100 “drill and kill” questions which build skill devoid of understanding. Our experience has been that students can do about 15-20 homework exercises a night so we very carefully chose smaller sets of questions which cover all of the necessary skills and get the students thinking more deeply about the Mathematics involved.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available. This textbook has been used in classes at:Boise State University,Claremont McKenna College,University of Minnesota, University of Puget Sound, Western Connecticut State University, Whitman College.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
OpenIntro Statistics covers a first course in statistics, providing a rigorous introduction to appliedstatistics that is clear, concise, and accessible. This book was written with the undergraduate levelin mind, but it’s also popular in high schools and graduate courses.We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. • Statistics is an applied field with a wide range of practical applications.• You don’t have to be a math guru to learn from real, interesting data.• Data are messy, and statistical tools are imperfect. But, when you understand the strengthsand weaknesses of these tools, you can use them to learn about the world.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
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e-book
Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus. The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation. In addition to the paper homework sets, algorithmetically generated online homework is available as part of a complete course shell package, which also includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the WAMAP.org template course list. For those located elsewhere, you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
This free online textbook (e-book in webspeak) is a one semester course in basic analysis. This book started its life as my lecture notes for Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of Wisconsin-Madison (UW-Madison). A prerequisite for the course is a basic proof course. It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school, but also as a first semester of a more advanced course that also covers topics such as metric spaces.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Functions of real variables Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
In writing this book, care was taken to use language and examples that gradually wean students from a simpleminded mechanical approach andmove them toward mathematical maturity. We also recognize that many students who hesitate to ask for help from an instructor need a readable text, and we have tried to anticipate the questions that go unasked. The wide range of examples in the text are meant to augment the "favorite examples" that most instructors have for teaching the topcs in discrete mathematics. To provide diagnostic help and encouragement, we have included solutions and/or hints to the odd-numbered exercises. These solutions include detailed answers whenever warranted and complete proofs, not just terse outlines of proofs. Our use of standard terminology and notation makes Applied Discrete Structures a valuable reference book for future courses. Although many advanced books have a short review of elementary topics, they cannot be complete. The text is divided into lecture-length sections, facilitating the organization of an instructor's presentation.Topics are presented in such a way that students' understanding can be monitored through thought-provoking exercises. The exercises require an understanding of the topics and how they are interrelated, not just a familiarity with the key words. An Instructor's Guide is available to any instructor who uses the text. It includes: Chapter-by-chapter comments on subtopics that emphasize the pitfalls to avoid; Suggested coverage times; Detailed solutions to most even-numbered exercises; Sample quizzes, exams, and final exams. This textbook has been used in classes atCasper College (WY), Grinnell College (IA), Luzurne Community College (PA), University of the Puget Sound (WA).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
- Resource Type:
- e-book
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e-book
In many introductory level courses today, teachers are challenged with the task of fitting in all of the core concepts of the course in a limited period of time. The Introductory Statistics teacher is no stranger to this challenge. To add to the difficulty, many textbooks contain an overabundance of material, which not only results in the need for further streamlining, but also in intimidated students. Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students' maturity level. Over time the core content of this course has developed into a well-defined body of material that is substantial for a one-semester course. Shafer and Zhang believe that the students in this course are best served by a focus on that core material and not by an exposure to a plethora of peripheral topics. Therefore in writing Introduction to Statistics they have sought to present only the core concepts and use a wide-ranging set of exercises for each concept to drive comprehension. As a result Introduction to Statistics is a smaller and less intimidating textbook that trades some extended and unnecessary topics for a better-focused presentation of the central material. You will not only appreciate the depth and breadth of exercises in Introduction to Statistics, but you will also like the close attention to detail that Shafer and Zhang have paid to the student and instructor solutions manuals. This is one of few books on the market where the textbook authors have written the solutions manuals to maintain the integrity of the material. In addition, in order to facilitate the use of technology with the book the authors included “large data set exercises,” where appropriate, that refer to large data sets that are available on the web, and for which use of statistical software is necessary.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
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e-book
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines. Used as a standalone textbook, Intermediate Algebra offers plenty of review as well as something new to engage the student in each chapter. Written as a blend of the traditional and graphical approaches to the subject, this textbook introduces functions early and stresses the geometry behind the algebra. While CAS independent, a standard scientific calculator will be required and further research using technology is encouraged. Intermediate Algebra is written from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success. A more modernized element, embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. Therefore, this text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today. The importance of Algebra cannot be overstated; it is the basis for all mathematical modeling used in all disciplines. After completing a course sequence based on Elementary and Intermediate Algebra, students will be on firm footing for success in higher-level studies at the college level.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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e-book
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student's place, and have chosen to err on the side of too much detail rather than not enough. An elementary text can't be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging. An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and definitions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Differential equations Partial Boundary value problems
- Resource Type:
- e-book
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e-book
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well. The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures. There are a few sections that are marked with a “(∗),” indicating that the material covered in that section is a bit technical, and is not needed else- where. There are many examples in the text, which form an integral part of the book, and should not be skipped. There are a number of exercises in the text that serve to reinforce, as well as to develop important applications and generalizations of, the material presented in the text. Some exercises are underlined. These develop important (but usually simple) facts, and should be viewed as an integral part of the book. It is highly recommended that the reader work these exercises, or at the very least, read and understand their statements. In solving exercises, the reader is free to use any previously stated results in the text, including those in previous exercises. However, except where otherwise noted, any result in a section marked with a “(∗),” or in §5.5, need not and should not be used outside the section in which it appears. There is a very brief “Preliminaries” chapter, which fixes a bit of notation and recalls a few standard facts. This should be skimmed over by the reader. There is an appendix that contains a few useful facts; where such a fact is used in the text, there is a reference such as “see §An,” which refers to the item labeled “An” in the appendix.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Algebra Textbooks Computer science -- Mathematics
- Resource Type:
- e-book
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e-book
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late, since we prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications–least squares and singular values. These are a fun way to end any lecture course. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
-
e-book
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are fully interactive in the HTML format and included in print in the PDF; the text is open source, and interested users can gain access to the original source files on GitHub; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; following the WeBWorK exercises in each section, there are several challenging problems that require students to connect key ideas and write to communicate their understanding.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis. This book proposes that an effective way to motivate these definitions is to tell one of the stories (there are many) of the historical development of the subject, from its intuitive beginnings to modern rigor. The definitions and techniques are motivated by the actual difficulties encountered by the intuitive approach and are presented in their historical context. However, this is not a history of analysis book. It is an introductory analysis textbook, presented through the lens of history. As such, it does not simply insert historical snippets to supplement the material. The history is an integral part of the topic, and students are asked to solve problems that occur as they arise in their historical context. This book covers the major topics typically addressed in an introductory undergraduate course in real analysis in their historical order. Written with the student in mind, the book provides guidance for transforming an intuitive understanding into rigorous mathematical arguments. For example, in addition to more traditional problems, major theorems are often stated and a proof is outlined. The student is then asked to fill in the missing details as a homework problem.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
Introductory Statistics follows the scope and sequence of a one-semester, introduction to statistics course and is geared toward students majoring in fields other than math or engineering. This text assumes students have been exposed to intermediate algebra, and it focuses on the applications of statistical knowledge rather than the theory behind it. The foundation of this textbook is Collaborative Statistics, by Barbara Illowsky and Susan Dean, which has been widely adopted. Introductory Statistics includes innovations in art, terminology, and practical applications, all with a goal of increasing relevance and accessibility for students. We strove to make the discipline meaningful and memorable, so that students can draw a working knowledge from it that will enrich their future studies and help them make sense of the world around them. The text also includes Collaborative Exercises, integration with TI-83,83+,84+ Calculators, technology integration problems, and statistics labs. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
-
e-book
Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of Openstax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. Openstax will also be releasing College Algebra and Algebra and Trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 14. More information, including free downloads of .pdf versions of the text, is available at www.apexcalculus.com.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
This text, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course in linear algebra for science and engineering students who have an understanding of basic algebra. All major topics of linear algebra are available in detail, as well as proofs of important theorems. In addition, connections to topics covered in advanced courses are introduced. The text is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the text. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations Textbooks Boundary value problems
- Resource Type:
- e-book
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e-book
This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students' problem-solving and writing skills.Open SUNY Textbooks is an open access textbook publishing initiative established by State University of New York libraries and supported by SUNY Innovative Instruction Technology Grants. This initiative publishes high-quality, cost-effective course resources by engaging faculty as authors and peer-reviewers, and libraries as publishing service and infrastructure. The pilot launched in 2012, providing an editorial framework and service to authors, students and faculty, and establishing a community of practice among libraries. Participating libraries in the 2012- 2013 pilot include SUNY Geneseo, College at Brockport, College of Environmental Science and Forestry, SUNY Fredonia, Upstate Medical University, and University at Buffalo, with support from other SUNY libraries and SUNY Press. More information can be found at http://textbooks.opensuny.org.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
- Resource Type:
- e-book
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e-book
Mathematical Reasoning: Writing and Proofis designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples. Develop the ability to read and understand written mathematical proofs. Develop talents for creative thinking and problem solving. Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics. Better understand the nature of mathematics and its language. This text also provides students with material that will be needed for their further study of mathematics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
Calculus is about the very large, the very small, and how things change—the surprise is that something seemingly so abstract ends up explaining the real world. This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems. One learns calculus by doing calculus, and so this course is based around doing practice problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
-
e-book
Prealgebra 2e is designed to meet scope and sequence requirements for a one-semester prealgebra or basic math course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty. The first edition of Prealgebra by OpenStax is available in web view in the ancillaries.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Arithmetic Algebra Textbooks
- Resource Type:
- e-book
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e-book
Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.Algebra and Trigonometry guides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
-
e-book
College Algebra provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of programs.College Algebraguides and supports students with differing levels of preparation and experience with mathematics. Ideas are presented as clearly as possible, and progress to more complex understandings with considerable reinforcement along the way. A wealth of examples – usually several dozen per chapter – offer detailed, conceptual explanations, in order to build in students a strong, cumulative foundation in the material before asking them to apply what they've learned. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
-
e-book
These are notes for a course in precalculus, as it is taught at New York City College of Technology - CUNY (where it is offered under the course number MAT 1375). Our approach is calculator based. For this, we will use the currently standard TI-84 calculator, and in particular, many of the examples will be explained and solved with it. However, we want to point out that there are also many other calculators that are suitable for the purpose of this course and many of these alternatives have similar functionalities as the calculator that we have chosen to use. An introduction to the TI-84 calculator together with the most common applications needed for this course is provided in appendix A. In the future we may expand on this by providing introductions to other calculators or computer algebra systems. This course in precalculus has the overarching theme of “functions.” This means that many of the often more algebraic topics studied in the previous courses are revisited under this new function theoretic point of view. However, in order to keep this text as self contained as possible we always recall all results that are necessary to follow the core of the course even if we assume that the student has familiarity with the formula or topic at hand. After a first introduction to the abstract notion of a function, we study polynomials, rational functions, exponential functions, logarithmic functions, and trigonometric functions with the function viewpoint. Throughout, we will always place particular importance to the corresponding graph of the discussed function which will be analyzed with the help of the TI-84 calculator as mentioned above. These are in fact the topics of the first four (of the five) parts of this precalculus course. In the fifth and last part of the book, we deviate from the above theme and collect more algebraically oriented topics that will be needed in calculus or other advanced mathematics courses or even other science courses. This part includes a discussion of the algebra of complex numbers (in particular complex numbers in polar form), the 2-dimensional real vector space R 2 sequences and series with focus on the arithmetic and geometric series (which are again examples of functions, though this is not emphasized), and finally the generalized binomial theorem.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra Textbooks
- Resource Type:
- e-book
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e-book
This is a "first course" in the sense that it presumes no previous course in probability. The mathematical prerequisites are ordinary calculus and the elements of matrix algebra. A few standard series and integrals are used, and double integrals are evaluated as iterated integrals. The reader who can evaluate simple integrals can learn quickly from the examples how to deal with the iterated integrals used in the theory of expectation and conditional expectation. Appendix B provides a convenient compendium of mathematical facts used frequently in this work. And the symbolic toolbox, implementing MAPLE, may be used to evaluate integrals, if desired. In addition to an introduction to the essential features of basic probability in terms of a precise mathematical model, the work describes and employs user defined MATLAB procedures and functions (which we refer to as m-programs, or simply programs) to solve many important problems in basic probability. This should make the work useful as a stand-alone exposition as well as a supplement to any of several current textbooks. Most of the programs developed here were written in earlier versions of MATLAB, but have been revised slightly to make them quite compatible with MATLAB 7. In a few cases, alternate implementations are available in the Statistics Toolbox, but are implemented here directly from the basic MATLAB program, so that students need only that program (and the symbolic mathematics toolbox, if they desire its aid in evaluating integrals). Since machine methods require precise formulation of problems in appropriate mathematical form, it is necessary to provide some supplementary analytical material, principally the so-called minterm analysis. This material is not only important for computational purposes, but is also useful in displaying some of the structure of the relationships among events.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Probabilities MATLAB Textbooks
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration. OpenStax College has compiled many resources for faculty and students, from faculty-only content to interactive homework and study guides.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
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e-book
Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Bayesian statistical decision theory Python (Computer program language) Textbooks
- Resource Type:
- e-book
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e-book
Think Stats is an introduction to Probability and Statistics for Python programmers. Think Stats emphasizes simple techniques you can use to explore real data sets and answer interesting questions. The book presents a case study using data from the National Institutes of Health. Readers are encouraged to work on a project with real datasets. If you have basic skills in Python, you can use them to learn concepts in probability and statistics. Think Stats is based on a Python library for probability distributions (PMFs and CDFs). Many of the exercises use short programs to run experiments and help readers develop understanding.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Textbooks Statistics -- Computer programs
- Resource Type:
- e-book
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e-book
This book focuses on the discrete Fourier transform (DFT), discrete convolution, and, particularly, the fast algorithms to calculate them. These topics have been at the center of digital signal processing since its beginning, and new results in hardware, theory and applications continue to keep them important and exciting. This book uses an index map, a polynomial decomposition, an operator factorization, and a conversion to a filter to develop a very general and efficient description of fast algorithms to calculate the discrete Fourier transform (DFT). The work of Winograd is outlined, chapters by Selesnick, Pueschel, and Johnson are included, and computer programs are provided.
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Fourier transformations Textbooks
- Resource Type:
- e-book
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e-book
Applied Combinatorics is an open-source textbook for a course covering the fundamental enumeration techniques (permutations, combinations, subsets, pigeon hole principle), recursion and mathematical induction, more advanced enumeration techniques (inclusion-exclusion, generating functions, recurrence relations, Polyá theory), discrete structures (graphs, digraphs, posets, interval orders), and discrete optimization (minimum weight spanning trees, shortest paths, network flows). There are also chapters introducing discrete probability, Ramsey theory, combinatorial applications of network flows, and a few other nuggets of discrete mathematics. Applied Combinatorics began its life as a set of course notes we developed when Mitch was a TA for a larger than usual section of Tom's MATH 3012: Applied Combinatorics course at Georgia Tech in Spring Semester 2006. Since then, the material has been greatly expanded and exercises have been added. The text has been in use for most MATH 3012 sections at Georgia Tech for several years now. Since the text has been available online for free, it has also been adopted at a number of other institutions for a wide variety of courses. In August 2016, we made the first release of Applied Combinatorics in HTML format, thanks to a conversion of the book's source from LaTeX to MathBook XML. An inexpensive print-on-demand version is also available for purchase. Find out all about ways to get the book. Since Fall 2016, Applied Combinatorics has been on the list of approved open textbooks from the American Institute of Mathematics. Applied Combinatorics is open source and licensed under the Creative Commons Attribution-ShareAlike 4.0 International License (CC-BY-SA).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Combinatorial analysis Graph theory Textbooks
- Resource Type:
- e-book
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e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
- Resource Type:
- e-book
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e-book
The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."
- Subjects:
- Management and Mathematics and Statistics
- Keywords:
- Industrial management -- Statistical methods Commercial statistics Textbooks
- Resource Type:
- e-book
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e-book
You are probably asking yourself the question, "When and where will I use statistics?". If you read any newspaper or watch television, or use the Internet, you will see statistical information. There are statistics about crime, sports, education, politics, and real estate. Typically, when you read a newspaper article or watch a news program on television, you are given sample information. With this information, you may make a decision about the correctness of a statement, claim, or "fact." Statistical methods can help you make the "best educated guess."
- Subjects:
- Management and Mathematics and Statistics
- Keywords:
- Industrial management -- Statistical methods Commercial statistics Textbooks
- Resource Type:
- e-book
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e-book
Calculus: Early Transcendentals, originally by D. Guichard, has been redesigned by the Lyryx editorial team. Substantial portions of the content, examples, and diagrams have been redeveloped, with additional contributions provided by experienced and practicing instructors. This approachable text provides a comprehensive understanding of the necessary techniques and concepts of the typical Calculus course sequence, and is suitable for the standard Calculus I, II and III courses. To practice and develop an understanding of topics, this text offers a range of problems, from routine to challenging, with selected solutions. As this is an open text, instructors and students are encouraged to interact with the textbook through annotating, revising, and reusing to your advantage. Suggestions for contributions to this growing textbook are welcome. Lyryx develops and supports open texts, with editorial services to adapt the text for each particular course. In addition, Lyryx provides content-specific formative online assessment, a wide variety of supplements, and in-house support available 7 days/week for both students and instructors.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style. Learn how to predict system outputs from measured data using a detailed step-by-step process to develop, train, and test reliable regression models. Key modeling and programming concepts are intuitively described using the R programming language. All of the necessary resources are freely available online.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Linguistics -- Statistical methods R (Computer program language) Mathematical linguistics
- Resource Type:
- e-book
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e-book
Applied Finite Mathematics covers topics including linear equations, matrices, linear programming, the mathematics of finance, sets and counting, probability, Markov chains, and game theory.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
This book is meant to be rigorous, conservative, elementary and minimalist. At the same time it includes about the maximum what students can absorb in one semester. Approximately one-third of the material used to be covered in high school, but not any more.The present book is based on the courses given by the author at the Pennsylvania State University as an introduction to the foundations of geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular,they are familiar with the real numbers and continuity. It makes it possible to cover the material faster and in a more rigorous way than it could be done in high school.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Geometry Plane Textbooks
- Resource Type:
- e-book
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e-book
My Math GPS: Elementary Algebra Guided Problem Solving is a textbook that aligns to the CUNY Elementary Algebra Learning Objectives that are tested on the CUNY Elementary Algebra Final Exam (CEAFE). This book contextualizes arithmetic skills into Elementary Algebra content using a problem-solving pedagogy. Classroom assessments and online homework are available from the authors.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
-
e-book
Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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e-book
I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hyperreals. The reader interested in questions of foundations should consult books such asAbraham Robinson's Non-standard Analysis or Robert Goldblatt's Lectures onthe Hyperreals. Secondly, I have aimed the text primarily at readers who already have somefamiliarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace istoo fast for most of those without some acquaintance with the basic notions of calculus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Textbooks
- Resource Type:
- e-book
-
e-book
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
-
e-book
This is a new approach to an introductory statistical inference textbook, motivated by probability theory as logic. It is targeted to the typical Statistics 101 college student, and covers the topics typically covered in the first semester of such a course. It is freely available under the Creative Commons License, and includes a software library in Python for making some of the calculations and visualizations easier.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical statistics Textbooks
- Resource Type:
- e-book
-
e-book
This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Algebra Textbooks Geometry
- Resource Type:
- e-book
-
e-book
Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Functional analysis Textbooks
- Resource Type:
- e-book
-
e-book
This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Textbooks
- Resource Type:
- e-book
-
e-book
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively. The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject. This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Geometry
- Resource Type:
- e-book
-
e-book
Intermediate Algebra 2e is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses. The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Algebra Textbooks
- Resource Type:
- e-book
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