- 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.

- 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%.

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. |