Trent University
Mathematics 2200H
Mathematical Reasoning
Archive Page
MATH 2200H is an introduction to the basics of handling abstractions and doing mathematical proofs while acquiring familiarity with a number of basic concepts, drawn from logic, set theory, number theory, combinatorics, and analysis, which are used in many mathematical fields.
Fall 2024
- MATH 2200H Course Outline [Unofficial summary of the syllabus.]
- A recommended book:
- Handouts:
- Assignment # 1,
2,
3,
4,
5,
6,
2π,
7,
8,
9,
10,
11,
12,
and Solutions to Assignment #
1,
2,
3,
4,
5,
6,
7,
8,
10,
11
- Take-Home Final Examination
- Some of the lectures were recorded, but too many were not. Please see the sets of recordings from preceding years below for fairly complete sets of recordings.
Fall 2023
- MATH 2200H Course Outline [Unofficial summary of the syllabus.]
- The nominal textbook:
- Handouts:
- Assignment # 1,
2,
3,
4,
5,
6,
τ,
7,
8,
π2,
9,
10,
11,
12,
and Solutions to Assignment #
1,
2,
3,
4,
5,
6,
7,
8,
10,
11
- Take-Home Final Examination
- Lecture recordings (all in webm format):
- 2023-09-07 - Introduction and a Knights and Knaves puzzle.
Handouts: A Knights and Knaves Puzzle,
Polya’s Problem Solving Principles
- 2023-09-11 [recording failed] - A little set theory, including defining ordered pairs and functions.
- 2023-09-12 - Relations, including linear orders and equivalence relations.
- 2023-09-14 - An informal introduction to propositional logic.
- 2023-09-18 - A formal language for propositional logic and deductions in it.
- 2023-09-19 - The Deduction Theorem for propositional logic.
- 2023-09-21 - First-order logic and a language for set theory.
- 2023-09-25 - A language for set theory redux and axioms for first-order logic.
- 2023-09-26 - Some axioms for set theory.
Handout: The Zermelo-Fraenkel Axioms of Set Theory
- 2023-09-28 - Tutorial for Assignment #3.
Assignment #3
- 2023-10-03 - Construction of the natural numbers.
- 2023-10-02 and 2023-10-5 were missed due to illness. The following lectures from the previous year were provided as partial replacements:
- 2023-10-10 - Addition of natural numbers is associative and commutative
- 2023-10-12 - Multiplication of natural numbers, cancellation laws, and defining the integers.
- 2023-10-16 - Axioms for the integers, arithmetic operations, and divisibility.
- 2023-10-17 - Divisibility and the Division and Euclidean algorithms.
- 2023-10-19 [recording failed] - Prime numbers, divisibility and prime numbers, and factorization.
- 2023-10-30 - Modular arithmetic via equivalence classes.
- 2023-11-02 - The Chinese Remainder Theorem.
- 2023-11-06 - The rational numbers via equivalence classes, and arithmetic operations on them.
- 2023-11-07 - Countability and embedding countable linear orders into the rationals.
- 2023-11-09 - Defining the real numbers via Dedekind cuts or schnitts, the linear order on the real numbers, suprema and infima.
- 2023-11-13 - The linear order on the real numbers is complete, and the Monotone Convergence Theorem.
- 2023-11-14 - Addition on the real numbers and its properties.
- 2023-11-16 [recording failed] - Multiplication on the real numbers and alternate ways to define the real numbers.
- 2023-11-20 - Cardinality and Cantor's Theorem.
- 2023-11-21 - The Schroeder-Bernstein Theorem.
- 2023-11-23 - The Axiom of Choice, and defining the ordinal numbers.
- 2023-11-27 - The union of a set of ordinals is an ordinal.
- 2023-11-28 - Finishing the proof that the union of a set of ordinals is an ordinal, and of a related lemma.
- 2023-11-30 - Addition on the ordinals and some propertoes thereof.
- 2023-12-04 - Multiplication on the ordinals, the Well-Ordering Theorem, and the cardinal hierarchy.
Fall 2022
- MATH 2200H Course Outline [Unofficial summary of the syllabus.]
- There is no textbook, but these two books are worth a read:
- Polya’s Problem Solving Principles
- The Greek Alphabet
- Assignment # 1,
2,
3,
4,
5,
6,
41,
7,
8,
9,
10,
11,
12
and Solutions to Assignment #
1,
2,
3,
4,
5,
6,
7,
8,
9,
10
- Take-Home Final Examination
- Lecture recordings [in webm format]:
Fall 2021
- MATH 2200H Course Outline [Unofficial summary of the syllabus.]
- The textbook: A Gentle Introduction to the Art of Mathematics [Version 3.1], by Joseph Fields.
Licensed under the GNU Free Documentation License, version 1.3 or later.
- Polya’s Problem Solving Principles
- The Greek Alphabet
- Assignment # 1,
2,
3,
4,
5,
6,
π+e,
7,
8,
9,
10,
11,
Bonus
and Solutions to Assignment #
2,
3,
4,
5,
6
- Take-Home Final Examination
- Lectures [All in webm format.]
Fall 2020
- MATH 2200H Course Outline
- The textbook: A Gentle Introduction to the Art of Mathematics [Version 3.1], by Joseph Fields.
Licensed under the GNU Free Documentation License, version 1.3.
- Polya’s Problem Solving Principles
- The Greek Alphabet
- Lectures and notes:
- Problem Solving - video, notes
- Divisibility - video, notes
- Irrationals - video, notes
- Propositional Logic - video, notes
- Propositional Logic II - video, notes
- First-Order Logic - video, notes
- First-Order Logic II - video, notes
- Set Theory - video, notes
- Set Theory II - video, notes
- Set Theory III - video, notes
- Set Theory IV - video, notes
- Natural Numbers - video, notes
- Natural Numbers II - video, notes
- Natural Numbers III - video, notes
- Natural Numbers IV - video, notes
- The Integers - video, notes
- The Integers II - video, notes
- The Integers III - video, notes
- The Integers IV - video, notes
- The Rationals - video, notes
- The Rationals II - video, notes
- The Rationals III - video, notes
- Real Numbers - video, notes
- Real Numbers II - video, notes
- Real Numbers III - video, notes
- Ordinals - video, notes
- Ordinals II - video, notes
- Ordinals III - video, notes
- Cardinals - video, notes
- Cardinals II - video, notes
- Cardinals III - video, notes
- Cardinals IV - video, notes
- Assignment # 1,
2,
3,
4,
5,
6,
τ,
7,
8,
9,
10,
11,
and Solutions to Assignment #
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11.
- Take-home Final Examination
Fall 2019
- MATH 2200H Course Outline
- The textbook: A Gentle Introduction to the Art of Mathematics [Version 3.1], by Joseph Fields.
- Polya’s Problem Solving Principles
- The Greek Alphabet
- Assignment # 1,
2,
3,
4,
4 make-up,
5,
5 make-up,
6,
7,
8,
9,
10,
11,
12,
Extra,
and Solutions to Assignment #
1,
2,
3,
4,
5,
6,
8,
9,
10
- Take-Home Final Examination [Due Wednesday, 18 December, or two weeks from receipt, whichever is earlier..]
Fall 2017
- MATH 2200H Course Outline
- The textbook: A Gentle Introduction to the Art of Mathematics [Version 3.1], by Joseph Fields.
- Assignment # 1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
and Solutions to Assignment # 1,
2,
3,
4,
5,
6,
8,
9,
10.
- Take-Home Final Examination [Due Saturday, 16 December.]
Fall 2016
- MATH 2200H Course Outline
- Assignment # 1,
2,
3,
4,
5,
6,
τ,
7,
8,
9,
10,
11
and Solutions to Assignment # 1,
2,
3,
4,
5,
6
- Take-Home Final Examination [Due Friday, 16 December.]
- A Couple of Problems stolen from Lewis Carroll.
Fall 2015
- MATH 2200H Course Outline
- Assignment # 1,
2,
3,
4,
5,
6,
τ,
7,
8,
9,
10,
11
- Take-Home Final Examination [Due Friday, 18 December, 2015.]
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Maintained by Stefan Bilaniuk. Last updated 2025-05-14.
