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Giáo trình, tài liệu tham khảo và tài nguyên học tập mở.
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Discrete Stochastic Processes
Robert Gallager · Massachusetts Institute of Technolog
Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This text aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding.
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The Physics of Waves
Howard Georgi · Harvard University
This text will provide you with the concepts and mathematical tools necessary to understand and explain a broad range of vibrations and waves. You will learn that waves come from many interconnected (coupled) objects when they are vibrating together. We will discuss many of these phenomena, along with related topics, including mechanical vibrations and waves, sound waves, electromagnetic waves, optics, and gravitational waves.
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Linear Algebra with Applications
W. Keith Nicholson · University of Calgary
Có trong mục lục: 12.C: Mathematical Induction · 1.00: Exercises for Mathematical Induction
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Business Calculus with Excel
Mike May, S.J. & Anneke Bart · Saint Louis University
This text is intended for a one semester calculus course for business students with the equivalent of a college algebra prerequisite. Rather than being a three-semester engineering calculus course that has been watered down to fit into one semester it is designed for the business students.
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Combinatorics and Graph Theory
David Guichard · Whitman College
Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics.Graph theory is concerned with various types of networks, or really models of networks called graphs. These are not the graphs of analytic geometry, but what are often described as "points connected by lines''.
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Differential Equations and Linear Algebra
Anup Lamichhane · Oho Northern University
In this book, you will learn key techniques for solving differential equations that arise in science and engineering applications. You will also build a strong foundation in linear algebra concepts that support these methods.
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An Inquiry-Based Approach to Abstract Algebra
Dana Ernst · Northern Arizona University
Có trong mục lục: 9.02: A.2- Fancy Mathematical Terms · 9.03: A.3- Definitions in Mathematics
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Foundations of Computation
Carol Critchlow & David J. Eck · Hobart and William Smith Colleges
Có trong mục lục: 1.08: Mathematical Induction
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Fundamentals of Matrix Algebra
Gregory Hartman · Virginia Military Institute
This text deals with matrix algebra, as opposed to linear algebra. Without arguing semantics, I view matrix algebra as a subset of linear algebra, focused primarily on basic concepts and solution techniques. There is little formal development of theory and abstract concepts are avoided. This is akin to the master carpenter teaching his apprentice how to use a hammer, saw and plane before teaching how to make a cabinet.
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Corequisite Precalculus
Katherine Skelton · Highline College
This course includes, but not limited to piece-wise, composite, inverse, polynomial, rational, exponential, and logarithmic functions. Also discussed are properties of functions, their relationship to equations and inequalities, as well as applications, and circles.
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Calculus Made Easy
Silvanus P. Thompson · City and Guilds Technical College
Calculus Made Easy is a book on infinitesimal calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject. Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern nonstandard analysis and smooth infinitesimal analysis.
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Manchester University Physical Chemistry I (CHEM 341)
Kathy Davis · Manchester University
Textbook for CHEM 341 at Manchester University (Physical Chemistry I). Foundations of quantum mechanics for describing atomic structure, molecular motion and chemical bonding, with specific applications to spectroscopy and chemical reactivity. Prerequisite(s): CHEM 113 (General Chemistry II), MATH 122 (Calculus II).
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College Algebra for Liberal Arts and Humanities
Leif Jordan · College of the Desert
A College Level Algebra text designed for students in the Liberal Arts and Humanities. Topics include: Linear, Quadratic, Rational, Exponential and Logarithmic Equations, Inequalities, Graphs and Functions with applications in business, the arts and social sciences. Conic sections, sequences, series, the binomial theorem and some mathematical history are also included.
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Early Childhood Education: STEM (NWTC)
Vicki Tanck · Northeast Wisconsin Technical College
Có trong mục lục: 05: Early Math Experiences · 5.01: Importance of Early Childhood Mathematics and Developing Number Sense
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Introduction to Matrix Algebra
Autar Kaw · University of South Florida
This book is an extended primer for undergraduate Matrix Algebra. The book is either to be used as a refresher material for students who have already taken a course in Matrix Algebra or as a just-in-time tool if the burden of teaching Matrix Algebra has been distributed to several courses.
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First-Semester Abstract Algebra: A Structural Approach
Jessica K. Sklar · Pacific Lutheran University
This text is specifically designed to suit a single-semester introductory abstract course, rather than to be a comprehensive reference source.
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An Introduction to Number Theory
J. J. P. Veerman · Portland State University
These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed. Chapters 1-6 represent approximately 1 trimester of the course. Eventually we intend to publish a full year (3 trimesters) course on number theory.
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College Algebra
Jay Abramson · Arizona State University
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebraoffers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
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Introduction to Statistics (RRCC)
Mathematics Department · Red Rocks Community College
This student-centered, open-source stats textbook builds conceptual understanding through real data, visuals, and interactive tools. Covering core topics like sampling, inference, and regression, it features step-by-step explanations, a semester-long housing project, and digital-friendly delivery. Designed for clarity, engagement, and flexibility, it's ideal for both students and instructors seeking practical, adaptable statistics resources.
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About Writing - A Guide
Robing Jeffrey · Klamath Community College
This writer’s reference condenses and covers everything a beginning writing student needs to successfully compose college-level work, including the basics of composition, grammar, and research. It is broken down into easy-to-tackle sections, while not overloading students with more information than they need. Great for any beginning writing students or as reference for advanced students!