Temperance (detail) Pieter Bruegel the Elder, 1560. 
MAT 511 Fundamental Concepts of Mathematics

Index Course Description Syllabus and Schedule 




9/6  Introduction and Administrivia. Inductive vs. Deductive reasoning. Brief historical overview of the rise and importance of mathematical proof and logic. Review of propositional logic and introduction to quantifiers.  Chapter 1 of the text.  None assigned. 
9/13  Logic and Proofs.  Read all of chapter 1 in the text. Read Ch. 2 as preparation for next week.  Homework 1, in
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9/20  More on Proofs. Set Theory. The Peano Axioms.  Ch 2.  Homework 2, in
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9/27  Review of proof methods, Mathematical Induction.  Section 2.4.  Homework 3, in
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10/4  More on Induction, Counting.  Section 2.5, 2.6  Homework 4, in
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10/11  Relations and partitions  Sections 3.1,3.2, and 3.3  Homework 5, in
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10/18  More on Relations  3.4, 3.5  Homework 6, in
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10/25  Functions  chapter 4  Homework 7, in
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11/1  more Functions.  the rest of chapter 4  Homework 8, in
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11/8  Cardinality  Sections 5.1, 5.2, 5.3  Homework 9, in
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11/15  Construction of the Integers, Rationals, and Reals. Proof that the reals are an uncountable set. CantorBernsteinSchroeder Theorem  Section 5.4  Homework 10 in
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11/22   
11/29  Algebraic structures; Groups, subgroups, operationpreserving maps (homomorphisms)  Sections 6.1, 6.2, 6.3, 6.4  Homework 11 in
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12/6  
12/13 