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Abstract Algebra: Theory and Applications

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Abstract Algebra: Theory and Applications

Thomas Judson · University of Puget Sound · 2016

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly. Until recently most abstract algebra texts included few if any applications. However, one of the major problems in teaching an abstract algebra course is that for many students it is their first encounter with an environment that requires them to do rigorous proofs. Such students often find it hard to see the use of learning to prove theorems and propositions; applied examples help the instructor provide motivation. This text contains more material than can possibly be covered in a single semester. Certainly there is adequate material for a two-semester course, and perhaps more; however, for a one-semester course it would be quite easy to omit selected chapters and still have a useful text. The order of presentation of topics is standard: groups, then rings, and finally fields. Emphasis can be placed either on theory or on applications. A typical one-semester course might cover groups and rings while briefly touching on field theory, using Chapters 1 through 6, 9, 10, 11, 13 (the first part), 16, 17, 18 (the first part), 20, and 21. Parts of these chapters could be deleted and applications substituted according to the interests of the students and the instructor. A two-semester course emphasizing theory might cover Chapters 1 through 6, 9, 10, 11, 13

Free Documentation License (GNU)AlgebraPure 0 views
An Open Guide to Data Structures and Algorithms

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An Open Guide to Data Structures and Algorithms

Paul Bible; Lucas Moser; Mia Scarlato · PALNI · 2023

This textbook serves as a gentle introduction for undergraduates to theoretical concepts in data structures and algorithms in computer science while providing coverage of practical implementation (coding) issues. The field of computer science (CS) supports a multitude of essential technologies in science, engineering, and communication as a social medium. The varied and interconnected nature of computer technology permeates countless career paths making CS a popular and growing major program. Mastery of the science behind computer science relies on an understanding of the theory of algorithms and data structures. These concepts underlie the fundamental tradeoffs that dictate performance in terms of speed, memory usage, and programming complexity that separate novice programmers from professional practitioners.

CC BYComputer Science 0 views
Agent-Based Evolutionary Game Dynamics

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Agent-Based Evolutionary Game Dynamics

Luis Izquierdo; Segismundo Izquierdo; William Sandholm · University of Wisconsin - Madison · 2024

This book is a guide to implement and analyze simple agent-based evolutionary models using NetLogo. All the models we implement are agent-based, i.e. individual agents and their interactions are explicitly represented in the models. To formalise agents’ interactions we use the basic framework of Evolutionary Game Theory. NetLogo is a multi-agent programmable modeling environment used by hundreds of thousands of students, teachers and researchers all around the globe. No coding experience is necessary to fully understand the contents of this book.

CC BYComputer Science 0 views
Introduction to Computer Science

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Introduction to Computer Science

Dr. Jean-Claude Franchitti; Amal Alhosban; Mark Buckler; Joanna Gilberti · OpenStax, Rice University

Introduction to Computer Science provides a comprehensive foundation in core computer science concepts and principles, aligning with the scope and sequence of most introductory computer science courses. The offering serves as an engaging entry point for students pursuing diverse fields of study and employment, including computer science, business, engineering, data science, social sciences, and related disciplines. By addressing a broad learner audience—ranging from computer science majors to non-majors—the book offers a thorough introduction to computational thinking and its applications across multiple domains. Introduction to Computer Science is designed to be both interactive and practical, focusing on real-world applications that showcase how core computer science concepts can be used to solve complex problems. Students will explore foundational concepts, such as algorithms, data structures, computer systems organization, and software development, using an array of engaging, hands-on activities. Introduction to Computer Science also includes advanced topics such as machine learning, cybersecurity, and cloud computing, ensuring students have a solid foundation for continued study and future professional success. The offering integrates meaningful learning experiences through chapter-based scenarios, problem-solving exercises, embedded coding activities, and project-based assessments that encourage students to apply what they learn in authentic contexts. The material also includes an array of industry insights and explorations of emerging technology trends in order to provide a holistic approach to learning that extends beyond theory.

CC BY-NC-SAComputer Science 0 views
ENG-001A: Composition and Reading

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ENG-001A: Composition and Reading

Jill Bonds · Coalinga College

In the contents: 2.4.03: In College Everythings an Argument- A Guide for Decoding College Writing Assignments

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Child Growth & Development Remix 2026

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Child Growth & Development Remix 2026

Kim Martin · Copper Mountain College

In the contents: 2.02: Psychosocial Theory · 2.03: Behaviorist Theory · 2.04: Social Cognitive Theory

CC0 / Public domainSocial Sciences 0 views
General Psychology for Honors Students

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General Psychology for Honors Students

Kate Votaw · University of Missouri–St. Louis

In the contents: 1.04: Freud And Psychoanalytic Theory · 20.02: Encoding And Storage- How Our Perceptions Become Memories · 28.03: Erik Erikson's Stage Theory Of Lifespan Development

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Introduction to Psychology (Lumen - Complete)

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Introduction to Psychology (Lumen - Complete)

LibreTexts

In the contents: 4.05: The History of PsychologyPsychoanalytic Theory and Gestalt Psychology · 10.03: Encoding

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Biopsychology

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Biopsychology

Open Education Resource Initative · OERI

In the contents: 18.09: Chapter 10- The Psychology of Memory Encoding Storage and Retrieval · 18.14: Chapter 14- Mirror Neurons Theory of Mind Social Cognition and Neuroscience of Its Disorders

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Physiological Psychology (IVC PSYCH003)

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Physiological Psychology (IVC PSYCH003)

Ivette Merced · Irvine Valley College

In the contents: 6.20.09: Chapter 10- The Psychology of Memory Encoding Storage and Retrieval · 6.20.14: Chapter 14- Mirror Neurons Theory of Mind Social Cognition and Neuroscience of Its Disorders

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Electrical Engineering

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Electrical Engineering

Don Johnson · Rice University

In the contents: 4.06: Encoding Information in the Frequency Domain · 6.21: Source Coding Theorem · 6.23: Subtlies of Coding

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Abstract Algebra: Theory and Applications

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Abstract Algebra: Theory and Applications

Thomas W. Judson · Stephen F. Austing State University

In the contents: 08: Algebraic Coding Theory · 8.05: Efficient Decoding · 23: Galois Theory

GNU FDLAbstract and Geometric AlgebraMathematics 0 views
Discrete Structures

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Discrete Structures

Laurie Lacey · SUNY Schenectady County Community College

In the contents: 05: Set Theory · 5.S: Set Theory (Summary) · 08: Topics in Number Theory

Mathematics 0 views
Psychology

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Psychology

Noba · LibreTexts

In the contents: 5.3: Memory (Encoding Storage Retrieval) · 7.4: Theory of Mind

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Friendly Introduction to Mathematical Logic

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Friendly Introduction to Mathematical Logic

Christopher Leary & Lars Kristiansen · SUNY Geneseo & University of Oslo

In the contents: 5.05: Coding - Naively · 5.06: Coding Is Representable · 5.12: Coding Deductions

CC BY-NC-SAMathematical Logic and ProofMathematics 0 views
Biology

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Biology

John W. Kimball · Tufts University & Harvard University

In the contents: 6.01: One Gene - One Enzyme Theory · 19.1.09: Barcoding

CC BYIntroductory and General BiologyBiology 0 views
Quantum Tutorials

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Quantum Tutorials

Frank Rioux · College of Saint Benedict/Saint John's University

In the contents: 1.51: Quantum Theory Wave-Particle Duality and the Mach-Zehnder Interferometer · 1.95: What Part of the Quantum Theory Dont You Understand · 3.31: Quantum Mechanics Group Theory and C60

CC BYPhysical and Theoretical Chemistry Textbook MapsChemistry 0 views
Learning Statistics with R - A tutorial for Psychology Students and other Beginners

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Learning Statistics with R - A tutorial for Psychology Students and other Beginners

DJ Navarro · University of New South Wales

In the contents: 7.02: Transforming and Recoding a Variable · 9.03: Basic Probability Theory

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Introduction to Statistics with R

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Introduction to Statistics with R

Edward Chi · Cerritos College

In the contents: 7.03: Basic Probability Theory · 17.02: Transforming and Recoding a Variable

Statistics 0 views
General Biology

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General Biology

Boundless · LibreTexts

In the contents: 4.03: Studying Cells - Cell Theory · 13.01: Chromosomal Theory and Genetic Linkage · 13.1A: Chromosomal Theory of Inheritance

CC BY-SAIntroductory and General BiologyBiology 0 views