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MA111: Introduction to Mathematical Reasoning
Sections
Course Introduction
Unit 1: Logic
Unit 2: Sets
Unit 3: Introduction to Number Theory
Unit 4: Rational Numbers
Unit 5: Mathematical Induction
Unit 6: Relations and Functions
Unit 7: Sets, Part II
Unit 8: Combinatorics
Course Feedback Survey
Certificate Final Exam
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MA111: Introduction to Mathematical Reasoning
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MA111: Introduction to Mathematical Reasoning
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-- Course Introduction --
-- Unit 1: Logic --
-- 1.1: Sudoku and Latin Squares --
-- 1.2: Ken-Ken --
-- 1.3: SET --
-- 1.4: Other Brain Teasers --
-- 1.4.1: Truth Tellers and Liars --
-- 1.4.2: Coin Weighing Puzzles --
-- 1.5: Propositional Logic --
-- 1.5.1: Compound Proposition --
-- 1.5.2: Truth Tables --
-- 1.6: Predicate Logic --
-- 1.6.1: Modus Ponens and Modus Tollens --
-- 1.6.2: Proofs by Contradiction --
-- 1.6.3: Problem Solving Strategies --
-- 1.6.4: Contrapositive and Equivalent Forms --
-- Unit 1 Assessment --
Unit 1 Assessment
-- Unit 2: Sets --
-- 2.1: What Is a Set? Set Builder Notation --
-- 2.1.1: The Empty Set, the Universal Set --
-- 2.1.2: Sets with Sets as Members --
-- 2.2: Building New Sets from Given Sets --
-- 2.2.1: Properties of Union, Intersection, and Complementation --
-- 2.2.2: The (Boolean) Algebra of Subsets of a Set --
-- 2.2.3: Using Characteristic Functions to Prove Properties of Sets --
-- 2.3: The Cartesian Product of Two or More Sets --
-- 2.3.1: The Disjoint Union and Addition --
-- 2.3.2: The Cartesian Product and Multiplication --
-- 2.4.1: The Cardinality of the Power Set of a Set --
-- 2.4.2: The Formula |A| + |B| = |A ⋃ B| + |A ⋂ B| --
-- Unit 2 Assessment --
Unit 2 Assessment
-- Unit 3: Introduction to Number Theory --
-- 3.1: Place Value Notation --
-- 3.2: Prime Numbers --
-- 3.2.1: An Infinitude of Primes --
-- 3.2.2: Conjectures about Primes --
-- 3.2.2.1: The Twin Prime Conjecture --
-- 3.2.2.2: Goldbach's Conjecture --
-- 3.2.2.3: The Riemann Hypothesis --
-- 3.3: Fundamental Theorem of Arithmetic (FTA) --
-- 3.4: Modular Arithmetic, the Algebra of Remainders --
-- 3.4.1: Division by 3, 9, and 11 --
-- 3.4.2: Building the Field Z? --
-- 3.4.3.1: The Addition of Remainders --
-- 3.4.3.2: The Multiplication of Remainders --
-- 3.5.1: The Floor and the Ceiling Functions --
-- 3.5.2: The Greatest Common Divisor (GCD) and Least Common Multiple (LCM) of Two Integers --
-- 3.5.3: The Sigma-Function, Summing Divisors --
-- 3.6: The Euclidean Algorithm --
-- 3.6.1: Another Look at the Division Algorithm --
-- 3.6.2: Solving Ax + By = C over the Integers --
-- Unit 4: Rational Numbers --
-- 4.1: Fractions and Rational Numbers Are Not the Same --
-- 4.2: Representing Rational Numbers as Decimals --
-- 4.3.1: The Square Roots of 2, 3, and 6 are All Irrational Numbers --
-- 4.3.2: Density of Irrational Numbers --
-- 4.3.3: Algebraic versus Transcendental Numbers --
-- 4.4: The Field of Rational Numbers --
-- Unit 5: Mathematical Induction --
-- 5.1: Mathematical Induction Is Equivalent to the Well-Ordering Property of N --
-- 5.2.1: Sums and Products --
-- 5.2.2: Divisibility --
-- 5.2.3: Recursively Defined Functions --
-- Unit 5 Assessment --
Unit 5 Assessment
-- Unit 6: Relations and Functions --
-- 6.1: Binary Relations on a Set A --
-- 6.2.1: Relations that Are Functions --
-- 6.2.2: Injections, Surjections, and Bijections --
-- 6.3: Equivalence Relations --
-- 6.4: Partial Orderings --
-- Unit 6 Assessment --
Unit 6 Assessment, Part 1
Unit 6 Assessment, Part 2
-- Unit 7: Sets, Part II --
-- 7.1: Cantor Diagonalization Theorem: The Existence of Uncountable Sets of Real Numbers --
-- 7.1.1: Proof of the Theorem --
-- 7.1.2: Even the Cantor Set Is Uncountable, the Base-3 Connection with the Cantor Ternary Set --
-- 7.1.3: Other Examples of Uncountable Subsets of R --
-- 7.2: The Rational Numbers Are Countable --
-- 7.2.1: The Proof --
-- 7.2.2: The Algebraic Numbers Are Countable --
-- 7.3: Other Bijections --
-- Unit 7 Assessment --
Unit 7 Assessment, Part 1
Unit 7 Assessment, Part 2
-- Unit 8: Combinatorics --
-- 8.1: Counting Problems as Sampling Problems with Conditions on the Structure of the Sample --
-- 8.2: The Inclusion-Exclusion Principle --
-- 8.2.1: The Case with Just Two Sets --
-- 8.2.2: The Proof --
-- 8.2.3: Other Examples --
-- 8.3: The Pigeon-Hole Principle (PHP) --
-- 8.3.1: The Standard Principle --
-- 8.3.2: Using the PHP Idea in Other Settings --
-- Course Feedback Survey --
-- Certificate Final Exam --
MA111: Certificate Final Exam
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Unit 1 Assessment
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Unit 1 Assessment
Unit 2 Assessment
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Unit 2 Assessment
Unit 5 Assessment
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Unit 5 Assessment
Unit 6 Assessment
Quiz
Unit 6 Assessment, Part 1
Quiz
Unit 6 Assessment, Part 2
Unit 7 Assessment
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Unit 7 Assessment, Part 1
Quiz
Unit 7 Assessment, Part 2
Certificate Final Exam
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MA111: Certificate Final Exam
Quiz Unit 1 Assessment