Overview and course content
The focus of this class is learning how to read and write mathematical proofs. The mathematical content, while important, is secondary to the reading and writing goals. Consequently, the standards from writing in this class will be higher than in other math classes you might have taken in the past. Students are expected to memorize definitions and statements of theorems.Content: The following topics will be covered:
- Introduction to logic: propositional calculus, quantifiers.
- Proof techniques: simple examples of mathematical proofs; induction
- Elementary number theory: construction of integers, rational and real numbers; prime factorization.
- Sets and functions: surjecions, injections, bijections, cardinality of a set.
- Infinite sets: countable and uncountable.
Prerequisites: These vary depending on your major or minor.
Math, IMME, STAT, STEMED-PRE or STEMED-BS: C-or better in 2153, 2162.xx, 2173, or 2182H; or credit for 254.xx, 263.xx or 263.01H.
CIS, CSE or ECE: C-or better in both CSE 2321 and: C-or better in 1152, 1161.xx, 1172, 1181H, 1534, or 1544; or credit for 153.xx, 154, 162.xx, or 162.01H.
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Syllabus and references
Textbook: Neil Falkner, The Fundamentals of Higher Mathematics. Autumn 2024 edition. (A free pdf copy of the textbook will be posted on Carmen.)Back to Top
Exams
- Midterm 1: Monday September 30, 2024 (in class). Topics: HW 1-5.
- Midterm 2: Friday November 15, 2024 (in class). Topics: HW 6-10.
- Final exam (CUMULATIVE): Wednesday December 11, 2024 (2:00pm-3:45pm, location TBD) In addition to the previous topics, the final exam will include material from HW 11 and 12.
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Homework
There will be 12 homework problem sets. These will be posted as the semester progresses on Carmen. The lowest two homework score will be dropped.Homeworks will be submitted in person, in class. No late homework will be accepted without medical excuse.
Participants can work in teams, but individual solutions must be submitted for grading and credit.
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