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Courseware
This is a graduatelevel 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

ebook
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:
 ebook

ejournal
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:
 ejournal

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

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 handson 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

Courseware
This graduatelevel 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

Courseware
This graduatelevel 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 polynomialtime hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudorandomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Computational complexity
 Resource Type:
 Courseware

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 CalderonZygmund 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 nonlinear 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

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

Courseware
This course offers an indepth 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

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

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 goodnessoffit. 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

Courseware
This course provides a rigorous treatment of noncooperative 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 noncooperative foundations.
 Subjects:
 Economics and Mathematics and Statistics
 Keywords:
 Game theory
 Resource Type:
 Courseware

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

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

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

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 BlacScholes, and other equations are discussed.
 Subjects:
 Finance and Mathematics and Statistics
 Keywords:
 Business mathematics
 Resource Type:
 Courseware

Courseware
This PreCalculus 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

Courseware
UCI Math 2A is the first quarter in SingleVariable 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

Courseware
Math 2B is the second quarter of SingleVariable 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

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

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

Courseware
Statistics is the science that turns data into information and information into knowledge. This class covers applied statistical methodology from an analysisofdata 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

Courseware
How do populations grow? How do viruses spread? What is the trajectory of a glider? Many reallife 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 reallife 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 realworld problems.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Mathematical models
 Resource Type:
 Courseware

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, KahaneKhintchine inequality, Anderson’s inequality. Stochastic integration in Banach spaces I: γRadonifying operators, γboundedness, 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

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

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

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

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

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

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

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

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, leastsquares, 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 handson exercises using highlevel numerical software.
 Subjects:
 Mathematics and Statistics
 Keywords:
 Convex functions Mathematical optimization
 Resource Type:
 Courseware

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

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

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 pvalues 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

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 DSGA1001 Intro to Data Science, which covers some important, fundamental data science topics that may not be explicitly covered in this DSGA class (e.g. data cleaning, crossvalidation, 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

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

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

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

ebook
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, HeriotWatt 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:
 ebook

ebook
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 honorslevel 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 online text for each of these collections collections willmeet the Section 508 standards for accessibility. An online course based on the textbook was also developed by Illowsky and Dean. It has won an awardas the best online California community college course. The online course will be available at a later dateas a collection in Connexions, and each lesson in the online course will be linked to the online textbookchapter. The online course will include, in addition to expository text and examples, videos of courselectures in captioned and noncaptioned 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 (TI83 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 nonESL 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:
 ebook

ebook
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 openended). 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:
 ebook

ebook
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 earlyandoften approach to realworld 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:
 ebook

ebook
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:
 ebook

ebook
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 1520 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:
 ebook

ebook
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:
 ebook

ebook
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 nonlinear 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:
 ebook

ebook
This free online textbook (ebook 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 UrbanaChampaign (UIUC) in the fall semester of 2009, and was later enhanced to teach Math 521 at University of WisconsinMadison (UWMadison). 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:
 ebook

ebook
Precalculus: An Investigation of Functions is a free, open textbook covering a twoquarter precalculus 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 selfstudy 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:
 ebook