| Section 001 | Section 002 | |
| Instructor | Angela Kubena | Brian Lehmann |
| Office | 3839 East Hall | 5852 East Hall |
| Phone | 763-3249 | 763-2020 |
| akubena at umich dot edu | blehmann at umich dot edu | |
| Office Hours |
Monday 3-4, Wednesday 1:30-2:30, Thursday 2-3 | Monday 10-11, Thursday 1-2 and 3-4 |
This course is designed to serve as an introduction to the methods and concepts of abstract mathematics. A typical student entering this course has substantial experience in using complex mathematical (calculus) calculations to solve physical or geometrical problems, but is unused to analyzing carefully the content of definitions or the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis. Much of the reading, homework exercises, and exams consists of theorems (propositions, lemmas, etc.) and their proofs. The initial topics include ones common to every branch of mathematics: sets, functions (mappings), relations, and the common number systems (integers, rational numbers, real numbers, and complex numbers). These are then applied to the study of particular types of mathematical structures such as groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials. Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied.
MATH 217 or equivalent required as background. This sheet explains in more detail what you are expected to know.