Harvard University Summer School 2006

Mathematics S-101

Course Notes

Worksheets

You can download the in-class worksheets in pdf format here.
  • Worksheet 1. Axioms of integer arithmetic.
  • Worksheet 2. Integers (I). Mathematical induction and well-ordering.
  • Worksheet 3. Integers (II). The Division Algorithm.
  • Worksheet 4. Logic.
  • Worksheet 5. Sets (I): Set Operations and Maps.
  • Worksheet 6. Sets (II): Partitions and Equivalence Relations.
  • Worksheet 7. Topological Spaces.
  • Worksheet 8. Closed Sets.
  • Worksheet 9. The Euclidean Closure Operator.
  • Worksheet 10. Connected Sets.
  • Worksheet 11. Completeness of the Real Numbers.
  • Worksheet 12. Continuous Functions.
  • Worksheet 13. Limits and Continuity in Rn.
  • Worksheet 14. The Brouwer Theorem in One Dimension.
  • Worksheet 15. Topological Equivalence.
  • Worksheet 16. The Brouwer Fixed Point Theorem.

© 2006 President and Fellows of Harvard College