Projected Written Notes for Lectures for M 325K, Spring 2024

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Click on the Notes for the desired Lecture. The Lectures are listed in Chronological Order.

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• Lecture on the M 325K Canvas Course, the Syllabus, and the relationship "Congruence (mod n) and on "Defining Variables in a Proof" -- Tuesday, January 16. 2024
• Lecture on Sec 2.1 - Logic: Statement Forms, Truth Tables, Equivalent Statement Forms, and DeMorgan's Laws, and Conditional Statements -- Thursday, January 18, 2024
• Lecture on the Conditional (If-Then) Statement and Related Statements and a Congruence (mod n) Theorem -- Tuesday, January 23, 2024
• Lecture on Arguments in Logic and Predicate Calculus-- Thursday, January 25, 2024
• Lecture on Universal Conditionals, on Combining Quantifiers, and on Universal Arguments -- Tuesday, January 30, 2024
• Lecture on Deductions, on Writing Proofs, on Definitions, and on The Direct Proof Method -- Thursday, February 1, 2024
• Lecture on The Method of Direct Proof, Ground Rules of Proof Writing, and Divisibility -- Tuesday, February 6, 2024
• Lecture on Sec 4.4: Divisibility, the Quotient-Remainder Theorem, and the (n mod d) function -- Thursday, February 8, 2024
• Lecture on The Unique (Prime) Factorization Theorem, Theorems (NIB) 2 and 3, Proofs Using Division into Cases, and Proof-by-Contradiction-- Tuesday, February 13, 2024
• Lecture on More on Proof-by-Contradiction, Proof by Contraposition, and an Introduction to Mathematical Induction-- Tuesday, February 20, 2024
• Lecture on Mathematical Induction and on Strong Mathematical Induction -- Thursday, February 22, 2024
• Lecture on Strong Mathematical Induction and The Well-Ordering Principle of the Integers -- Tuesday, February 27, 2024
• Lecture on Sec 6.1, An Introduction to Set Theory -- Thursday, February 29, 2024
• Lecture on Writing Elemental Proofs in Set Theory -- Tuesday, March 5, 2024
• Lecture on Section 6.3 - Algebraic Proofs in Set Theory and Disproving a False Identity -- Thursday, March 7, 2024
• Lecture on Sections 8.1 and 8.2: Relations, Inverse Relations, and the Reflexive, Symmetric, and Transitive Properties which some relations have -- Tuesday, March 19, 2024
• Lecture on Section 8.3 - Equivalence Relations and Equivalence Classes and Proving Theorems about Equivalence Classes -- Tuesday, March 26, 2024
• Lecture on Section 8.4 (Epp's 4th Edition) - Modular Arithmetic: Theorems 8.4.1 and 8.4.3, and the Handout, "Alternate Versions of Examples ..." -- Thursday, March 28, 2024
• Lecture on Sec 8.5: The Euclidean Algorithm for Finding the GCD, and Sec 8.4 (Epp's 4th Edition): - Expressing the GCD(a,b) as as + bt, Modular Inverses, and Simple Congruences -- Tuesday, April 2, 2024
• Lecture on Section 8.4 (Epp's 4th Edition): Expressing the GCD(a,b) as as + bt, Modular Inverses, Congruences and Solving Simple Congruences and RSA Encryption and Decryption-- Thursday, April 4, 2024
• Lecture on Sections 7.1 & 7.2 - Functions in General and One-to-One Functions and Onto Functions -- Tuesday, April 9, 2024
• Lecture on Section 7.3 - Composition of Functions, Inverse Functions, and the "Test for a One-to-One Correspondence" - Thm (NIB) 10 -- Tuesday, April 16, 2024
• Lecture on Section 7.4 - Cardinality of Sets and "Notes on Cardinality" -- Thursday, April 18, 2024
• Lecture on Section 7.4 - More Notes on Cardinality -- Tuesday, April 23, 2024
• Lecture on Cardinality and the Continuum Hypothesis -- Thursday, April 25, 2024

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