Trent University

Mathematics 2200H

*Mathematical Reasoning*

Archive Page

- MATH 2200H Course Outline [Unofficial summary of the syllabus.]
- The nominal 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. - Supplementary materials for the textbook:

- A Gentle Introduction to the Art of Mathematics [Version 3.1], by Joseph Fields.
- Handouts:
- Assignment # 1,
2,
3,
4,
5,
6,
τ,
7,
8,
π
^{2}, 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.

- 2023-09-07 - Introduction and a Knights and Knaves puzzle.

- MATH 2200H Course Outline [Unofficial summary of the syllabus.]
- There is no textbook, but these two books are worth a read:
- 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. - Proofs: A Long-Form Mathematics Textbook, by Jay Cummings, ISBN 13: 9798595265973.

- 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,
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]:
- 2022-09-08:
*What can we deduce in a Minesweeper configuration?*[recording failed] - 2022-09-13:
*Baby Set Theory and the Natural Numbers* - 2022-09-14:
*Baby Set Theory and the Natural Numbers II* - 2022-09-15:
*Functions and Relations* - 2022-09-20:
*Propositional Logic* - 2022-09-21:
*Propositional Logic II* - 2022-09-22:
*Propositional Logic III* - 2022-09-27:
*First-Order Logic* - 2022-09-28:
*First-Order Logic II* - 2022-09-29:
*Natural Numbers* - 2022-10-04:
*Natural Numbers II* - 2022-10-05:
*Baby Number Theory* - 2022-10-06:
*Baby Number Theory II* - 2022-10-11:
*Baby Number Theory III* - 2022-10-12:
*Modular Arithmetic* - 2022-10-13:
*Modular Arithmetic II* - 2022-10-18:
*Defining the Integers* - 2022-11-01:
*Defining the Rational Numbers* - 2022-11-02:
*Defining the Rational Numbers II* - 2022-11-03:
*Defining the Rational Numbers III* - 2022-11-08:
*Properties of the Rationals* - 2022-11-09:
*Properties of the Rationals II*[recording failed] - 2022-11-10:
*Defining the Real Numbers*[poor audio] - 2022-11-15:
*Defining the Real Numbers II* - 2022-11-16:
*Defining the Real Numbers III* - 2022-11-17:
*Defining the Real Numbers IV* - 2022-11-22:
*Convergence of Sequences* - 2022-11-23:
*Convergence of Sequences II* - 2022-11-24:
*Convergence of Sequences III*[recording failed] - 2022-11-29:
*Convergence of Sequences IV* - 2022-11-30:
*Convergence of Sequences V & Cardinality* - 2022-12-01:
*Cardinality II*

- 2022-09-08:

- 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.]
- Problem Solving (2021-09-13) [First part of the lecture missing due to failure to start recording.]
- Working Through a Proof (2021-09-14)
- Propositional Logic (2021-09-15)
- Propositional Logic II (2021-09-20)
- Propositional Logic III and First-Order Logic (2021-09-21)
- First-Order Logic II (2021-09-22)
- Set Theory (2021-09-27)
- Set Theory II (2021-09-28)
- Set Theory III (2021-09-29)
*[Failed to record.]* - Set Theory IV (2021-10-05) notes
- Natural Numbers (2021-10-06) notes
- Natural Numbers II (2021-10-12)
- Natural Numbers III (2021-10-13
- Natural Numbers IV (2021-10-18)
- Integers (2021-10-19)
- Integers II (2021-10-20)
- Integers III (2021-11-02)
- Integers IV & Rationals (2021-11-03)
- Rationals II (2021-11-08)
- Rationals III (2021-11-09)
- Reals (2021-11-10)
- Reals II (2021-11-15)
- Reals III (2021-11-16)
*[Failed to record.]* - Reals IV (2021-11-17)
- Ordinals (2021-11-22)
- Ordinals II (2021-11-23)
- Ordinals III (2021-11-24)
- Ordinals IV (2021-11-29)
- Ordinals V (2021-11-30)
- Cardinals (2021-12-01)
- Cardinals II (2021-12-06)
- Cardinals III (2021-12-07)

- 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

- 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..]*

- 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.]*

- 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.

- 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.]*

Department of Mathematics Trent University

Maintained by Stefan Bilaniuk. Last updated 2023-12-18.