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Giáo trình, tài liệu tham khảo và tài nguyên học tập mở.
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An Introduction to Proof via Inquiry-Based Learning
Dana Ernst · Northern Arizona University
This book is intended to be used for a one-semester/quarter introduction to proof course (sometimes referred to as a transition to proof course). The purpose of this book is to introduce the reader to the process of constructing and writing formal and rigorous mathematical proofs. The intended audience is mathematics majors and minors. However, this book is also appropriate for anyone curious about mathematics and writing proofs.
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Transition to Higher Mathematics
Bob Dumas and John E. McCarthy · University of Washington and Washington University in St. Louis
Có trong mục lục: 1.5: Images and Inverses
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Gentle Introduction to the Art of Mathematics
Joseph Fields · Southern Connecticut State University
Có trong mục lục: 01: Introduction and Notation · 1.06: Rational And Irrational Numbers · 02: Logic and Quantifiers
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Friendly Introduction to Mathematical Logic
Christopher Leary & Lars Kristiansen · SUNY Geneseo & University of Oslo
Có trong mục lục: 01: Structures and Languages · 1.04: Terms and Formulas · 1.09: Substitutions and Substitutability
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Mathematical Reasoning - Writing and Proof
Ted Sundstrom · Grand Valley State University
Có trong mục lục: 01: Introduction to Writing Proofs in Mathematics · 1.01: Statements and Conditional Statements · 1.02: Constructing Direct Proofs
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MCC: MTH 220 - Discrete Math
Judy Dean · Monroe Community College
Có trong mục lục: 1.3: How to Read and Write Mathematics · 1.5: Introduction to Sets and Real Numbers · 2: Logic
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Proofs and Concepts - The Fundamentals of Abstract Mathematics
Dave Witte Morris & Joy Morris · University of Lethbridge
Có trong mục lục: 01: Propositional Logic · 1.01: Assertions deductions and validity · 1.02: Logic Puzzles
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Discrete Mathematics
Oscar Levin · University of Northern Colorado
Có trong mục lục: 0: Introduction and Preliminaries · 0.2: Mathematical Statements · 0.E: Introduction and Preliminaries (Exercises)
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Math for Educators (MATH 010A and 010B CID120)
Lynn Mann · LibreTexts
Có trong mục lục: 1.02: Understanding Mathematical Content Knowledge · 1.04: Common Core Standards for Mathematics · 1.4.01: Kindergarten Standards Overview
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Math 375: Pre-Calculus
Roy Simpson, Sangchin Sertich & Paige Buck-Moyer · Cosumnes River College
Có trong mục lục: 01: Triangles and Circles · 1.01: Angles and Basic Geometry · 1.1.01: Resources and Key Concepts
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A Spiral Workbook for Discrete Mathematics
Harris Kwong · State University of New York at Fredonia
Có trong mục lục: 1.03: How to Read and Write Mathematics · 02: Logic · 2.02: Conjunctions and Disjunctions
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Discrete Structures
Laurie Lacey · SUNY Schenectady County Community College
Có trong mục lục: 01: Introduction to Writing Proofs in Mathematics · 1.01: Statements and Conditional Statements · 1.02: Constructing Direct Proofs
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SMC: MATH 339 Discrete Mathematics
Rohatgi · Saint Mary's College
Có trong mục lục: 0: Introduction and Preliminaries · 0.2: Mathematical Statements · 0.E: Introduction and Preliminaries (Exercises)
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MAT 310 Bridge to Advanced Mathematics
Richard Hammack · Virginia Commonwealth University
Có trong mục lục: 02: Logic · 2.01: And Or Not · 2.05: Logical Equivalence
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Mathematics for Computer Science
Eric Lehman, F. Thomson Leighton, & Alberty R. Meyer · Google and Massachusetts Institute of Technology
Có trong mục lục: 01: Proofs · 01: Intro to Proofs · 1.06: Proving an If and Only If
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Elementary Foundations: An Introduction to Topics in Discrete Mathematics
Jeremy Sylvestre · University of Alberta Augustana
Có trong mục lục: 1.03: Logical Analysis · 1.04: Tautologies and contradictions · 02: Logical equivalence
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Mathematical Reasoning
Pamini Thangarajah · Mount Royal University
Có trong mục lục: 1.2: More on Logical Statements · 2.1: Subsets and Equality · 2.3: Venn Diagrams and Euler Diagrams
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Foundations of Computation
Carol Critchlow & David J. Eck · Hobart and William Smith Colleges
Có trong mục lục: 01: Logic and Proof · 1.01: Propositional Logic · 1.03: Application - Logic Circuits
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Delftse Foundations of Computation
Stefan Hugtenburg & Neil Yorke-Smith · Delft University of Technology
Có trong mục lục: 01: Logic · 1.01: Propositional Logic · 1.1.02: Logical operators
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Discrete Mathematics for Computer Science
Jin He · Fresno City College
Có trong mục lục: 01: Introduction to Propositional Logic · 1.04: Proving an If and Only If · 1.05: Proof by Cases