Discussion Schedule

Small group discussions are held at various times on Mondays, Tuesdays and Wednesdays in one of a number of smaller classrooms on the higher floors of the Lederle tower. Discussions are an essential aspect of the course, allowing students to meet with the TA (Laura) and talk about mathematics in a small setting. Students are required to choose a discussion section and attend every week. If you miss your discussion for any reason (e.g., school holiday, absence, etc.), you should attend another section. Homework will also be assigned and collected and quizzes will be given in discussion, so particular attention should be paid to attending discussions.

Exam Schedule

Homeworks and Quizzes

• • Homework problem sets will be assigned and collected weekly. Late problem sets are subjected to 50% penalty.

  • Quizzes will be given frequently in discussion sessions during the semester.

Grading

Your grade will be made up of the following components:

• • Three midterm exams - 15% each

  • The final exam - 25%

  • Homework - 20%

  • Quizzes and discussion - 10%

The total of these scores will be converted into a letter grade by the following scale:

Goals for Math 300

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 (Notes)

3. countable and uncountable sets

4. 1-1 and onto functions

5. equivalence relations

6. basic logic of truth tables

7. implications and proofs

B. Elementary Combinatorics:

1. basic principles of counting (Notes)

2. combinations (Notes)

3. well-ordering principle and induction (Notes)

4. recursion (Notes)

5. pigeon-hole principle (Notes)

C. Complex numbers: (Notes)

1. Definition and basic properties of complex numbers.

D. Basic topology: (Notes)

1. Metric spaces.

2. Topological spaces.

3. Continuous functions.

See the official syllabus for more details.

Problem Sets