College of the Holy Cross, Spring 2022
Syllabus for Math 243 (Mathematical Structures)
Professor Hwang, (rhymes with song)
Do not make travel plans that conflict with the midterm tests or your final exam. If an emergency prevents you from taking the final exam at the allotted time, speak to your Class Dean immediately to arrange for an incomplete grade, and to me to schedule a make-up exam.
The schedule below is subject to minor changes. Any substantial corrections will be announced by email and/or in class.
| Day | Date | Section | Topics |
| M | Jan 24 | Advising | |
| W | Jan 26 | Section 1.1 | Welcome and Introduction |
| F | Jan 28 | Section 1.1 | Statements and Truth Tables |
| M | Jan 31 | Section 1.2 | Quantified Statements |
| W | Feb 2 | Section 1.3 | Sets and Partitions |
| F | Feb 4 | Section 1.4 | Cartesian Products and Mappings |
| M | Feb 7 | Section 2.3 | Induction with Formulas |
| W | Feb 9 | Section 2.3 | Induction with Properties |
| F | Feb 11 | Section 7.1 | Rational Numbers |
| M | Feb 14 | Section 7.1 | Real Numbers and Inequalities |
| W | Feb 16 | Section 7.1 | Inequalities and Absolute Values |
| F | Feb 18 | Section 7.2 | Complex numbers |
| M | Feb 21 | Section 7.2 | Geometry of Complex Multiplication |
| W | Feb 23 | Section 7.2 | Cayley Tables, Roots of Unity |
| F | Feb 25 | Midterm 1 | |
| M | Feb 28 | Section 3.4 | Counting Subsets |
| W | Mar 2 | Section 7.3 | The Binomial Theorem |
| F | Mar 4 | Section 3.1 | Images and Preimages |
| M | Mar 7 | Spring Break | |
| W | Mar 9 | Spring Break | |
| F | Mar 11 | Spring Break | |
| M | Mar 14 | Section 3.2 | Surjectivity and Injectivity |
| W | Mar 16 | Section 3.2 | The Pigeonhole Principle |
| F | Mar 18 | Section 3.2 | Bijections and Cardinality |
| M | Mar 21 | Section 3.3 | Composition and Inverses |
| W | Mar 23 | Section 2.2 | The Division Algorithm |
| F | Mar 25 | Section 2.2 | Subgroups of the Integers |
| M | Mar 28 | Section 5.1 | Greatest Common Divisors |
| W | Mar 30 | Section 5.2 | Primes and Unique Factorization |
| F | Apr 1 | Midterm 2 | |
| M | Apr 4 | Section 4.1 | Equivalence Relations |
| W | Apr 6 | Section 6.1 | Modular arithmetic |
| F | Apr 8 | Section 6.2 | Units and Inverses |
| M | Apr 11 | Section 4.2 | Well-Definedness |
| W | Apr 13 | Section 4.2 | Induced Mappings |
| F | Apr 15 | Easter | |
| M | Apr 18 | Easter | |
| W | Apr 20 | Section 3.6,3.7 | Binary Operations |
| F | Apr 22 | Section 8.1 | Sets of Real Numbers |
| M | Apr 25 | Section 8.1 | Uncountable Sets |
| W | Apr 27 | Academic Conference | |
| F | Apr 29 | Midterm 3 | |
| M | May 2 | Section 8.2 | Suprema and Infima |
| W | May 4 | Section 8.2 | Completeness |
| F | May 6 | Section 8.2 | Real Square Roots |
| M | May 9 | Section 8.3 | The Archimedean Property |