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Mathematical Proofs · LearnSpace
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courseraМатематика

Mathematical Proofs

Курс от Case Western Reserve University
Средний≈ 19.7 чАнглийский
О курсеНавыкиПрограммаПреподаватели

О курсе

The objective of this course is to provide you with a basic understanding of what is involved with reading, understanding, thinking about, and doing mathematical proofs. The systematic approach presented here reduces the time and frustration involved in learning this type of thinking. You will also learn how to read and understand “condensed” proofs that are typically found in textbooks, journal articles, and other mathematical literature and used by professors in virtually all advanced math courses (such as discrete math, linear algebra, abstract algebra, and real analysis, for example).

Навыки, которые вы освоите

Deductive ReasoningLogical ReasoningAlgebraGeneral MathematicsComputational LogicMathematical Theory & AnalysisApplied MathematicsAdvanced MathematicsMathematics and Mathematical Modeling

Программа курса

15 модулей · 95 учебных материалов

01What is a Proof?11 материалов

Welcome to the Course!

Welcome from Dr. SolowВидеоCourse IntroductionЧтение1.1: The Definition of a Proof and an ImplicationВидео1.2: Using the Truth Table to Do a ProofВидео

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Daniel Solow

Professor

Mathematical Proofs
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Обучение на Coursera

≈ 19.7 ч

15 модулей

Язык: Английский

Часть программы вашего университета
Module 1.3: Watch Out for WordingВидео
1.4: What is a “Convincing Argument” and What is the Language of Mathematics?Видео
Module 1 Practice ExercisesЧтение
Solutions to Module 1 ExercisesЧтение
Need Help? Ask our AI Tutor-botPLUGIN
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Need extra help? Register for Professor Solow's Thursday evening office hoursPLUGIN
02The Forward-Backward Method6 материалов
2.1: The Idea of the Forward-Backward MethodВидео2.2: Details of the Backward ProcessВидео2.3: Details of the Forward ProcessВидео2.4: Writing and Reading a ProofВидеоModule 2 ExercisesЧтениеSolutions to Module 2 ExercisesЧтение
03Definitions and Mathematical Terminology 8 материалов
3.1: What is a Mathematical Definition?Видео3.2: Using a DefinitionВидео3.3: Notational Issues Associated with a DefinitionВидео3.4: Using Previous KnowledgeВидео3.5: Mathematical TerminologyВидеоModule 3 ExercisesЧтениеSolutions to Module 3 ExercisesЧтениеAssessment Exam 1Задание
04Quantifiers Part I: The Construction Method 6 материалов
4.1: The Existential Quantifier “There Is”Видео4.2: What is the Construction Method?Видео4.3: Reading a Proof that Uses the Construction MethodВидео4.4: Another Example of Using the Construction MethodВидеоModule 4 ExercisesЧтениеSolutions to Module 4 ExercisesЧтение
05Quantifiers Part II: The Choose Method 6 материалов
5.1: The Universal Quantifier “For All”Видео5.2: The Idea of the Choose Method?Видео5.3: Examples of Using the Choose Method?Видео5.4: Reading a Proof that Uses the Choose MethodВидеоModule 5 ExercisesЧтениеSolutions to Module 5 ExercisesЧтение
06Quantifiers Part III: Specialization7 материалов
6.1: How Specialization WorksВидео6.2: Some Examples of SpecializationВидео6.3: A Complete Example of SpecializationВидео6.4: Reading a Proof that Uses SpecializationВидеоModule 6 ExercisesЧтениеSolutions to Module 6 ExercisesЧтениеAssessment Exam 2Задание
07Quantifiers Part IV: Nested Quantifiers 5 материалов
7.1: The Rule for Working with Nested QuantifiersВидео7.2: Using Proof Techniques with Nested QuantifiersВидео7.3: Reading a Proof that Involves Nested QuantifiersВидеоModule 7 ExercisesЧтениеSolutions to Module 7 ExercisesЧтение
08Negations of Statements6 материалов
8.1: Rules for Writing the Negation of Statements Without QuantifiersВидео8.2: Rules for Writing the Negation of Statements With a Single QuantifierВидео8.3: Rules for Writing the Negation of Statements With Nested QuantifiersВидео8.4: The Negation of the Statement “A Implies B”: CounterexamplesВидеоModule 8 ExercisesЧтениеSolutions to Module 8 ExercisesЧтение
09The Contradiction Method 8 материалов
9.1: How and When to Use the Contradiction MethodВидео9.2: An Example of Using the Contradiction MethodВидео9.3: Another Example of Using the Contradiction MethodВидео9.4: Additional Uses of the Contradiction MethodВидео9.5: Reading a Proof that Uses the Contradiction MethodВидеоModule 9 ExercisesЧтениеSolutions to Module 9 ExercisesЧтениеAssessment Exam 3Задание
10The Contrapositive Method5 материалов
10.1: An Explanation of the Contrapositive MethodВидео10.2: An Example of the Contrapositive MethodВидео10.3: Reading a Proof that Uses the Contrapositive MethodВидеоModule 10 ExercisesЧтениеSolutions to Module 10 ExercisesЧтение
11The Uniqueness Methods6 материалов
11.1: The Forward Uniqueness MethodВидео11.2: The Backward Direct Uniqueness MethodВидео11.3: The Backward Indirect Uniqueness MethodВидео11.4 SummaryВидеоModule 11 ExercisesЧтениеSolutions to Module 11 ExercisesЧтение
12Induction7 материалов
12.1: How and When to Use the Induction MethodВидео12.2: An Example of InductionВидео12.3: Some Variations on InductionВидео12.4: Reading a Proof that Uses InductionВидеоModule 12 ExercisesЧтениеSolutions to Module 12 ExercisesЧтениеAssessment Exam 4Задание
13The Either/Or Methods5 материалов
13.1: The Either / Or Method in the Forward Process: Proof-By-CasesВидео13.2: The Either / Or Method in the Backward Process: Proof-By-EliminationВидео13.3: Additional Practice with the Either / Or MethodsВидеоModule 13 ExercisesЧтениеSolutions to Module 13 ExercisesЧтение
14The Max/Min Methods4 материалов
14.1: How and When to Use the Max / Min MethodsВидео14.2: Examples of the Max / Min MethodsВидеоModule 14 ExercisesЧтениеSolutions to Module 14 ExercisesЧтение
15Course Summary5 материалов
15.1: Summary of the Proof Techniques Видео15.2: A Final Example of How to Read a Proof ВидеоModule 15 ExercisesЧтениеSolutions to Module 15 ExercisesЧтениеAssessment Exam 5Задание