Search Results: Mathematics & Statistics

A Computational Introduction to Number Theory and Algebra

Victor Shoup, New York University

This introductory book emphasizes algorithms and applications, such as cryptography and error correcting codes, and is accessible to a broad audience. The presentation alternates between theory and applications in order to motivate and illustrate the mathematics. The mathematical coverage includes the basics of number theory, abstract algebra and discrete probability theory.

(0 reviews)

A First Course in Linear Algebra

Robert A. Beezer, University of Puget Sound

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.

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A Gentle Introduction to the Art of Mathematics

Joseph E. Fields, Southern Connecticut State University

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.

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Active Calculus

David Austin, Grand Valley State University
Matt Boelkins, Grand Valley State University
Steve Schlicker, Grand Valley State University

In Active Calculus, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore.

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Applied Discrete Structures

Alan Doerr, University of Massachusetts Lowell
Kenneth Levasseur, University of Massachusetts Lowell

As a general description one could say that discrete mathematics is the mathematics that deals with "separated" or discrete sets of objects rather than with continuous sets such as the real line.

(0 reviews)

Basic Analysis: Introduction to Real Analysis

JirĂ­ Lebl

This free online textbook (e-book in webspeak) is a one semester course in basic analysis.

(0 reviews)

Book of Proof

Dr. Richard Hammack, Virginia Commonwealth Univ.

Book of Proof is an introduction to the language and methods of mathematical proofs.  The text is meant to bridge the computational courses that students typically encounter in their first years of college (such as calculus or differential equations) to more theoretical, proof-based courses such as topology, analysis and abstract algebra.  Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

(0 reviews)

Calculus

Gilbert Strang, MIT

Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a straightforward introductory calculus textbook available free online to educators and self-learners alike. It is covers single variable and multivariable calculus, including applications.

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Calculus for the Life Sciences: A Modeling Approach Volume 1

James L. Cornette, Iowa State University
Ralph A. Ackerman, Iowa State University

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.

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Calculus for the Life Sciences: A Modeling Approach Volume 2

James L. Cornette, Iowa State University
Ralph A. Ackerman

This text is a product of a two-semester calculus course for life sciences students in which students gathered biological data in a laboratory setting that was used to motivate the concepts of calculus.  The book contains data from experiments, but does not require that students do laboratory experiments.

(0 reviews)

Collaborative Statistics

Susan Dean, De Anza College
Dr. Barbara Illowsky, De Anza College

Collaborative Statistics was developed over several years and has been used in regular and honors-level classroom settings and in distance learning classes. This textbook is intended for introductory statistics courses being taken by students at two– and four–year colleges 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.

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(3 reviews)

College Algebra

Dr. Carl Stitz, Lakeland Community College
Dr. Jeff Zeager, Lorain County Community College

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.

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(4 reviews)

College Trigonometry

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

Covers chapters 10-11 of Precalculus.

(0 reviews)

Combinatorics Through Guided Discovery

Kenneth P. Bogart

This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems.

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Elementary Algebra

John Redden, College of the Sequoias

Elementary Algebra, is an introductory text that focuses on the study of algebra at the beginning stages.  It assumes no prior algebraic experience and is intended for any student who needs build a strong algebraic foundation.  The book presents real world applications, setting a foundation for students to translate problems described in words into mathematical equations. The book illustrates the steps required to solve equations and interpret the results through the use of exercise sets and practice problems. The book stresses both the importance to solve problems correctly, and to learn to communicate those solutions to others.

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Elementary Differential Equations with Boundary Value Problems

William F. Trench, Trinity University

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation.

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Fundamentals of Mathematics

Denny Burzynski
Wade Ellis

Fundamentals of Mathematics is a work text that covers the traditional study in a modern prealgebra course, as well as the topics of estimation, elementary analytic geometry, and introductory algebra.

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Intermediate Algebra

John Redden, College of the Sequoias

Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study in applications found in most disciplines.

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Introduction to Probability

Dr. Charles M. Grinstead, Swarthmore College
Dr. J. Laurie Snell, Dartmouth College

This text is designed for an introductory probability course taken by sophomores, juniors, and seniors in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a ?rm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.

(0 reviews)

Introduction to Real Analysis

William F. Trench, Trinity University

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

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Introductory Statistics

Douglas S. Shafer, University of North Carolina
Zhiyi Zhang, University of North Carolina

Shafer and Zhang wrote Introductory Statistics by using their vast teaching experience to present a complete look at introductory statistics topics while keeping in mind a realistic expectation with respect to course duration and students’ maturity level.

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(3 reviews)

Linear Algebra

Dr Jim Hefferon, Saint Michael's College

This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications.

(0 reviews)

Linear Algebra

Andrew Waldon
David Cherney
Tom Denton

This book is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors.

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Math in Society

David Lippman

Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors.

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Mathematical Reasoning: Writing and Proof

Ted Sundstrom, Grand Valley State University

This textbook is designed for the first course in the college mathematics curriculum that introduces students to the process of constructing and writing proofs.

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OpenIntro Statistics

Christopher D. Barr, Harvard School of Public Health
David M. Diez, Harvard School of Public Health
Mine Cetinkaya-Rundel, Duke University

Our inaugural effort is OpenIntro Statistics. First and foremost, OpenIntro Statistics strives to be a complete introductory textbook of the highest caliber. Its core derives from the classic notions of statistics education and is extended by recent innovations.

The textbook meets high quality standards and has been used at Harvard, Princeton, and many other schools. We look forward to expanding the reach of the project and working with teachers from all colleges and schools.

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Precalculus

Carl Stitz, Lakeland Community College
Jeff Zeager, Lorain County Community College

College Algebra & Trigonometry

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Precalculus: An Investigation of Functions

David Lippman
Melonie Rasmussen

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry.

(0 reviews)

Vector Calculus

Michael Corral, Schoolcraft College

 This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

(0 reviews)

Whitman Calculus

Dr David Guichard, Whitman College

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.

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(4 reviews)


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