Instructor: Bill Meeks
Office: LGRT 1536
Phone: 545-4239 (office) 549-5204 (home)
email: bill@math.umass.edu
Office Hours: Thursdays, 9:30am-12:30pm in the Blue Wall
TA Brian Wilson Office Hours: Wednesdays, 2:30 - 3:30
in room LGRT 1322
Course Information
Click here for the class schedule.
Class lecture: Tuesdays and Thursdays 2:30-3:45 in LGRT 123
Discussion sections: Click here to see a list of discussion times.
Discussion rooms & times are stil not set. Check the discussions page.
Grading:
Three midterms - 45%
Final exam - 25%
Homework & discussion grade - 15%
Quizzes - 15%
Text: A packet of class notes is handed out the first day of class. Homework is included in the note packet, as well as copies of all the quizzes that will be given during the semester. The packet also contains a sample or "practice" midterm from each of the three sections of the notes that
are covering this semester. If you lose your copy and want to print another one, then here is a copy of the
pdf file.
I. Get some understanding and perspective on the general philosophy of mathematics from a mathematician's point of view.
II. Learn techniques of proof and the logic behind them.
III. Learn basic material for more advanced classes in analysis and algebra.
IV. Get practice in speaking mathematics and in giving proofs in front of class.
Basic Material to be covered:
A. Set Theory and logic:
1. unions and intersections
2. sizes of sets
3. countable and uncountable sets
4. 1-1 and onto functions
5. equivalence relations
6. basic logic of truth tables
7. implications and proofs
8. well-ordering principle and induction
B. Group theory:
1. definitions and basic properties of groups and subgroups
2. LaGrange's Theorem
3. homomorphisms, kernel, and image
4. isomorphism theorems and quotient groups
5. definitions of fields and vector space concepts like dimension and matrix representation for linear transformations
C. Metric and topological spaces:
1. the topology of metric spaces
2. basic definitions and results on open and closed sets
3. the concepts of connected and compact topological spaces
4. definition and properties of continuous functions
5. fundamental theorem of calculus