The Six Pillars of Calculus: Biology Edition
The Six Pillars of Calculus: Biology Edition

Author: Lorenzo Sadun

Publisher: American Mathematical Society

Published: 2023-05-19

Total Pages: 379

ISBN-13: 1470469960

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The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning—to focus on when and why to use the tools of calculus, not just on how to apply formulas. Modeling and differential equations are front and center. Solutions begin with numerical approximations; derivatives and integrals emerge naturally as refinements of those approximations. Students use and modify computer programs to reinforce their understanding of each algorithm. The Biology Edition of the Six Pillars series has been extensively field-tested at the University of Texas. It features hundreds of examples and problems specifically designed for students in the life sciences. The core ideas are introduced by modeling the spread of disease, tracking changes in the amount of $mathrm{CO}_{2}$ in the atmosphere, and optimizing blood flow in the body. Along the way, students learn about optimal drug delivery, population dynamics, chemical equilibria, and probability.

A Discrete Transition to Advanced Mathematics
A Discrete Transition to Advanced Mathematics

Author: Bettina Richmond

Publisher: American Mathematical Society

Published: 2023-08-25

Total Pages: 540

ISBN-13: 147047204X

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This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity. Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio. A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout. New features include a chapter on combinatorial geometry, a more in-depth treatment of counting, and over 365 new exercises.

An Introduction to Real Analysis
An Introduction to Real Analysis

Author: Yitzhak Katznelson

Publisher: American Mathematical Society

Published: 2024-05-22

Total Pages: 280

ISBN-13: 1470474212

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An Introduction to Real Analysis gives students of mathematics and related sciences an introduction to the foundations of calculus, and more generally, to the analytic way of thinking. The authors' style is a mix of formal and informal, with the intent of illustrating the practice of analysis and emphasizing the process as much as the outcome. The book is intended for use in a one- or two-term course for advanced undergraduates in mathematics and related fields who have completed two or three terms of a standard university calculus sequence.

Introduction to Quantum Algorithms
Introduction to Quantum Algorithms

Author: Johannes A. Buchmann

Publisher: American Mathematical Society

Published: 2024-03-18

Total Pages: 391

ISBN-13: 1470473984

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Quantum algorithms are among the most important, interesting, and promising innovations in information and communication technology. They pose a major threat to today's cybersecurity and at the same time promise great benefits by potentially solving previously intractable computational problems with reasonable effort. The theory of quantum algorithms is based on advanced concepts from computer science, mathematics, and physics. Introduction to Quantum Algorithms offers a mathematically precise exploration of these concepts, accessible to those with a basic mathematical university education, while also catering to more experienced readers. This comprehensive book is suitable for self-study or as a textbook for one- or two-semester introductory courses on quantum computing algorithms. Instructors can tailor their approach to emphasize theoretical understanding and proofs or practical applications of quantum algorithms, depending on the course's goals and timeframe.

Linear Algebra
Linear Algebra

Author: R¢bert Freud

Publisher: American Mathematical Society

Published: 2024-10-25

Total Pages: 318

ISBN-13: 147047736X

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This textbook invites readers to dive into the mathematical ideas of linear algebra. Offering a gradual yet rigorous introduction, the author illuminates the structure, order, symmetry, and beauty of the topic. Opportunities to explore, master, and extend the theory abound, with generous exercise sets embodying the Hungarian tradition of active problem-solving. Determinants, matrices, and systems of linear equations begin the book. This unique ordering offers insights from determinants early on, while also admitting re-ordering if desired. Chapters on vector spaces, linear maps, and eigenvalues and eigenvectors follow. Bilinear functions and Euclidean spaces build on the foundations laid in the first half of the book to round out the core material. Applications in combinatorics include Hilbert?s third problem, Oddtown and Eventown problems, and Sidon sets, a favorite of Paul Erd?s. Coding theory applications include error-correction, linear, Hamming, and BCH codes. An appendix covers the algebraic basics used in the text. Ideal for students majoring in mathematics and computer science, this textbook promotes a deep and versatile understanding of linear algebra. Familiarity with mathematical proof is assumed, though no prior knowledge of linear algebra is needed. Supplementary electronic materials support teaching and learning, with selected answers, hints, and solutions, and an additional problem bank for instructors.

Introduction to Mathematics
Introduction to Mathematics

Author: Scott A. Taylor

Publisher: American Mathematical Society

Published: 2023-09-13

Total Pages: 445

ISBN-13: 1470471884

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This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of mathematical history and culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge.

Applied Linear Algebra
Applied Linear Algebra

Author: Lorenzo Adlai Sadun

Publisher: American Mathematical Soc.

Published: 2007-12-20

Total Pages: 394

ISBN-13: 0821844415

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Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle. Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrodinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings. Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform. The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.

The Six Pillars of Calculus: Business Edition
The Six Pillars of Calculus: Business Edition

Author: Lorenzo Sadun

Publisher: American Mathematical Society

Published: 2023-05-12

Total Pages: 379

ISBN-13: 1470469952

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The Six Pillars of Calculus: Business Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning—to focus on when and why to use the tools of calculus, not just on how to apply formulas. Modeling and differential equations are front and center. Solutions begin with numerical approximations; derivatives and integrals emerge naturally as refinements of those approximations. Students use and modify computer programs to reinforce their understanding of each algorithm. The Business Edition of the Six Pillars series has been extensively field-tested at the University of Texas. It features hundreds of examples and problems designed specifically for business students. The core ideas are introduced by modeling market penetration of a new product, tracking changes in the national debt, and maximizing the profit of a business. Along the way, students learn about present value, consumer and producer surplus, amortization, and probability.

Calculus for Biology and Medicine
Calculus for Biology and Medicine

Author: Claudia Neuhauser

Publisher: Prentice Hall

Published: 2004

Total Pages: 0

ISBN-13: 9780130455161

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For a two-semester course in Calculus for Life Sciences. This text addresses the needs of students in the biological sciences by teaching calculus in a biological context without reducing the course level. It is a calculus text, written so that a math professor without a biology background can teach from it successfully. New concepts are introduced in a three step manner. First, a biological example motivates the topic; second, the topic is then developed via a simple mathematical example; and third the concept is tied to deeper biological examples. This allows students: to see why a concept is important; to understand how to use the concept computationally; to make sure that they can apply the concept.

Social Science Research
Social Science Research

Author: Anol Bhattacherjee

Publisher: CreateSpace

Published: 2012-04-01

Total Pages: 156

ISBN-13: 9781475146127

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This book is designed to introduce doctoral and graduate students to the process of conducting scientific research in the social sciences, business, education, public health, and related disciplines. It is a one-stop, comprehensive, and compact source for foundational concepts in behavioral research, and can serve as a stand-alone text or as a supplement to research readings in any doctoral seminar or research methods class. This book is currently used as a research text at universities on six continents and will shortly be available in nine different languages.