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
• 2.7 Tautologies and Contradictions
• 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
• 5.2 Proof by Contradiction
• 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%.