Digital library
Textbooks, references and open learning resources.
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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
In the contents: 1.5: Images and Inverses
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Gentle Introduction to the Art of Mathematics
Joseph Fields · Southern Connecticut State University
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 1.03: Logical Analysis · 1.04: Tautologies and contradictions · 02: Logical equivalence
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Mathematical Reasoning
Pamini Thangarajah · Mount Royal University
In the contents: 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
In the contents: 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
In the contents: 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
In the contents: 01: Introduction to Propositional Logic · 1.04: Proving an If and Only If · 1.05: Proof by Cases