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Video
Mathematics is not about following rules, it's about playing—and exploring, fighting, looking for clues, and sometimes even breaking things, according to Dan Finkel. In this playful, inspiring talk, the founder of Math for Love offers teachers and parents alike a five-step guide to sharing the beauty and playfulness of mathematical thinking with children.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics -- Study teaching
- Resource Type:
- Video
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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
A Cool, Brisk Walk Through Discrete Mathematics, an innovative and non-traditional approach to learning Discrete Math, is available for low cost from Blurb or via free download.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks Computer science -- Mathematics
- 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 First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically students will have taken calculus, but it is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Determinants and eigenvalues are covered along the way. A unique feature of this book is that chapters, sections and theorems are labeled rather than numbered. For example, the chapter on vectors is labeled "Chapter V" and the theorem that elementary matrices are nonsingular is labeled "Theorem EMN." Another feature of this book is that it is designed to integrate SAGE, an open source alternative to mathematics software such as Matlab and Maple. The author includes a 45-minute video tutorial on SAGE and teaching linear algebra. This textbook has been used in classes at: Centre for Excellence in Basic Sciences, Westmont College, University of Ottawa, Plymouth State University, University of Puget Sound, University of Notre Dame, Carleton University, Amherst College, Felician College, Southern Connecticut State University, Michigan Technological University, Mount Saint Mary College, University of Western Australia, Moorpark College, Pacific University, Colorado State University, Smith College, Wilbur Wright College, Central Washington U (Lynwood Center), St. Cloud State University, Miramar College, Loyola Marymount University.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable. It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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Video
What if we looked at Parkinson's as an neurological electrical problem? Brain researcher Eleftheria Pissadaki and her team study dopamine neurons, the neurons that selectively die during Parkinson's. They discovered that the bigger a neuron is, the more vulnerable it becomes because it simply requires more energy. This new insight is reframing the disease -- and by "finding the fuse box for each neuron" and figuring out how much energy it needs, may help us neuroprotect our brain cells.
- Subjects:
- Health Sciences and Mathematics and Statistics
- Keywords:
- Brain -- Diseases -- Research Brain -- Mathematical models
- Resource Type:
- Video
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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
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Video
In a lively show, mathemagician Arthur Benjamin races a team of calculators to figure out 3-digit squares, solves another massive mental equation and guesses a few birthdays. How does he do it? He’ll tell you.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mental arithmetic Mental calculators
- Resource Type:
- Video
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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 was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Precalculus Trigonometry Algebra 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
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
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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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e-book
We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods. (1) Statistics is an applied field with a wide range of practical applications. (2) You don't have to be a math guru to learn from real, interesting data. (3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world. Textbook overviewThe chapters of this book are as follows: 1. Data collection. Data structures, variables, and basic data collection techniques. 2. Summarizing data. Data summaries and graphics. 3. Probability. The basic principles of probability. 4. Distributions of random variables. Introduction to key distributions, and how the normal model applies to the sample mean and sample proportion. 5. Foundation for inference. General ideas for statistical inference in the context of estimating the population proportion. 6. Inference for categorical data. Inference for proportions using the normal and chisquare distributions. 7. Inference for numerical data. Inference for one or two sample means using the t distribution, and comparisons of many means using ANOVA. 8. Introduction to linear regression. An introduction to regression with two variables. Instructions are also provided in several sections for using Casio and TI calculators.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book
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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
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e-book
"This resource covers the following learning objectives: explain the uses and misuses of statistics
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Mathematical statistics
- Resource Type:
- e-book
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e-book
"We are often faced with questions concerning our finances: Am I saving enough to put my daughter through college? How much will my investment be worth five years from now? Should I pay down my mortgage with weekly or monthly payments? The mathematics of finance allows us to answer these and similar questions. This textbook aligns with Adult Basic Education (ABE) Advanced Level Mathematics"--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Business mathematics Mathematics Textbooks
- Resource Type:
- e-book
-
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
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e-book
"This is a textbook for first year Computer Science. Algorithms and Data Structures With Applications to Graphics and Geometry."--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Data structures (Computer science) Textbooks Algorithms
- Resource Type:
- e-book
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e-book
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Number theory Textbooks
- Resource Type:
- e-book
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Video
How do we make sense of a world that doesn't? By looking in unexpected places, says mathematician Eugenia Cheng. She explains how applying concepts from abstract mathematics to daily life can lead us to a deeper understanding of things like the root of anger and the function of privilege. Learn more about how this surprising tool can help us to empathize with each other.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics -- Social aspects Equality
- Resource Type:
- Video
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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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e-book
This is a free textbook teaching introductory statistics for undergraduates in Psychology. This textbook is part of a larger OER course package for teaching undergraduate statistics in Psychology, including this textbook, a lab manual, and a course website. All of the materials are free and copiable, with source code maintained in Github repositories.
- Subjects:
- Psychology and Mathematics and Statistics
- Keywords:
- Statistics Social sciences -- Statistical methods Textbooks Psychology
- Resource Type:
- e-book
-
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
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
-
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 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
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
"This is a course in undergraduate real analysis, also known as advanced calculus. The book works for both basic courses for students who do not necessarily wish to go to graduate school and also more advanced courses that prepare students for graduate study and cover topics such as metric spaces. A prerequisite for the course is a basic proof course. This book starts with analysis on the real line, going through sequences, series, and then into continuity, the derivative, and the Riemann integral using the Darboux approach. There are plenty of available detours along the way, or you can power through toward the metric spaces in chapter 7. The philosophy is that metric spaces are absorbed much better by the students after they have gotten comfortable with basic analysis techniques in the very concrete setting of the real line. As a bonus, the book can be used both by slower-paced, more concrete courses, as well as a faster-paced, more abstract courses for future graduate students"--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Functions of real variables Mathematical analysis
- Resource Type:
- e-book
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e-book
"This book is a continuation of Basic Analysis: Introduction to Real Analysis - Volume 1. Volume II continues into multivariable analysis, starting with differential calculus, including inverse and implicit function theorems, continuing with differentiation under the integral and path integrals, which are often not covered in a course like this, and multivariable Riemann integral. Finally, there is also a chapter on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier series. Together, the two volumes provide enough material for several different types of year-long sequences. A student who absorbs the first volume and the first three chapters of volume II should be more than prepared for real and complex analysis courses at the graduate level"--BCcampus website.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Functions of real variables Mathematical analysis
- Resource Type:
- e-book
-
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
-
Others
This sequence is ideal for students or early data science professionals who want to strengthen their knowledge of fundamental probability and statistics concepts. Mastery of Mathematical Fundamentals is a prerequisite.
- Course related:
- AMA1110 Basic Mathematics I – Calculus and Probability & Statistics
- Subjects:
- Finance and Mathematics and Statistics
- Keywords:
- Probabilities Mathematical statistics Business mathematics
- Resource Type:
- Others
-
Others
Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints. This technique has been useful for guiding quantitative decisions in business planning, in industrial engineering, and—to a lesser extent—in the social and physical sciences.
- Course related:
- AAE3009 Operations Research and Computational Analytics in Air Transport Operations
- Subjects:
- Mathematics and Statistics
- Keywords:
- Linear programming
- Resource Type:
- Others
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e-book
Business Mathematics was written to meet the needs of a twenty-first century student. It takes a systematic approach to helping students learn how to think and centers on a structured process termed the PUPP Model (Plan, Understand, Perform, and Present). This process is found throughout the text and in every guided example to help students develop a step-by-step problem-solving approach. This textbook simplifies and integrates annuity types and variable calculations, utilizes relevant algebraic symbols, and is integrated with the Texas Instruments BAII+ calculator. It also contains structured exercises, annotated and detailed formulas, and relevant personal and professional applications in discussion, guided examples, case studies, and even homework questions.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Business mathematics Textbooks
- Resource Type:
- e-book
-
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 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
-
e-book
Esta comunidad tiene como fin construir un texto base, que pretende ser la puerta de entrada al mundo de las matemáticas superiores y sus aplicaciones en el campo de las Ciencias de la Ingeniería.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Integral Calculus Differential calculus Textbooks
- Resource Type:
- e-book
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e-book
"In 2013, Lyryx forked the now-popular Calculus open textbook written by David Guichard. Michael Cavers of the University of Calgary, together with the Lyryx editorial team, further redeveloped the content, examples, diagrams, and overall look-and-feel of the book, making it more accessible to first year college and university students. Additional contributors have helped improve the content, including Mark Blenkinsop of Carleton University. In particular, there was the addition of an introductory chapter reviewing the fundamental topics required in a first semester Calculus course, and the paring down of topics that are typically beyond the scope of math and engineering service courses. Currently, the book covers the standard Calculus I and II courses, with Calculus III under development."--Open Textbook Library.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus 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
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
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
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
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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
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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
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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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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
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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
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