# Math 3310

• Classes start Mon Aug 28th; Mon, Wed, Fri 10:00--10:50.
• Location: Math 13.
• Office Hours: Mon, Wed, Fri; 11:00--12:00.
• Homework: Set periodically and posted to this website.
• Exams:
• The first midterm exam will be on Friday the 13th of October.
• The second midterm exam will be on Friday the 17th of November.
• The final will be on Monday the 11th of December from 1:30pm to 4:00pm.
• Syllabus:
• Textbook: Mathematical Proofs. A transition to advanced mathematics. Third edition. By Chartrand, Polimeni and Zhang.
• Outline: The purpose of the course is to introduce mathematics as a process of logical reasoning rather than merely calculation. We will study logic, the language of mathematics. We will learn what a proof in mathematics is, how to understand a written proof and how to construct our own. The topics from the book that I intend to cover are:
• 1.1 Describing a Set
• 1.2 Subsets
• 1.3 Set Operations
• 1.4 Indexed Collections of Sets
• 1.5 Partitions of Sets
• 1.6 Cartesian Products of Sets
• 2.1 Statements
• 2.2 The Negation of a Statement
• 2.3 The Disjunction and Conjunction of Statements
• 2.4 The Implication
• 2.5 More on Implications
• 2.6 The Biconditional
• 2.8 Logical Equivalence
• 2.9 Some Fundamental Properties of Logical Equivalence
• 2.10 Quantified Statements
• 2.11 Characterizations of Statements
• 3.1 Trivial and Vacuous Proofs
• 3.2 Direct Proofs
• 3.3 Proof by Contrapositive
• 3.4 Proof by Cases
• 4.1 Proofs Involving Divisibility of Integers
• 4.2 Proofs Involving Congruence of Integers
• 4.3 Proofs Involving Real Numbers
• 4.4 Proofs Involving Sets
• 4.5 Fundamental Properties of Set Operations
• 4.6 Proofs Involving Cartesian Products of Sets
• 5.1 Counterexamples
• 5.4 Existence Proofs
• 5.5 Disproving Existence Statements
• 6.1 The Principle of Mathematical Induction
• 6.2 A More General Principle of Mathematical Induction
• 6.3 Proof by Minimum Counterexample
• 8.1 Relations
• 8.2 Properties of Relations
• 8.3 Equivalence Relations
• 8.4 Properties of Equivalence Classes
• 8.5 Congruence Modulo n
• 8.6 The Integers Modulo n
• 9.1 The Definition of a Function
• 9.3 One-to-one and Onto Functions
• 9.4 Bijective Functions
• 9.5 Composition of Functions
• 9.6 Inverse Functions
• Note: This syllabus may be subject to modest alterations in content as the semester progresses. Some topics from chapters 10 and 11 will be covered if time permits.
• Assessment:
• Homework assignments will contribute to 10% of your grade. It is important that you hand them in on time.
• There will be two midterm exams. Each midterm exam will be worth 25% of your grade.
• There will be a final exam, which will be worth 40%.

 Homework Date due Q1.4, 1.8, 1.9. Fri 8th September. Q1.12, 1.14, 1.18, 1.24, 1.25, 1.30, 1.32. Fri 15th September. Q1.36, 1.40, 1.46, 1.48, 1.53. Fri 22nd September. Q1.60, 1.63, 1.66, 2.6, 2.11, 2.16, 2.18. Fri 29th September. Q2.32, 2.38, 2.44, 2.46, 2.52, 2.54. Fri 6th October. Q3.10, 3.16, 3.20, 3.26, 3.28, 4.2, 4.8. Fri 27th October. Q4.10, 4.18, 4.26, 4.28, 4.40, 4.44, 4.56, 4.70. Fri 3rd November. Q5.2, 5.4, 5.14, 5.18, 5.24, 5.28, 5.42. Fri 10th November. Q6.4, 6.16, 6.18, 6.20, 6.24, 6.34, 6.40. Fri 1st December.
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