Math/CCS: Introduction to Higher Mathematics
Course Information:
- Professor: Padraic Bartlett.
- Email: padraic at math dot ucsb dot edu.
- Syllabus: linked here.
Lecture Notes:
- Weeks 0-1: The art and language of proof.
- Week 1: Proof techniques.
- Week 2: Sizes of infinity.
- Weeks 3-4: Set theory.
- Week 5: Equivalence relations.
- Week 6: Measure, integration and limits.
- Weeks 7-8: Constructible numbers.
- Week 8: Transcendental numbers.
- Week 9: Linear algebra (crash course.)
- Week 9: Field extensions.
- Week 10: Complex numbers.
Homework:
- Homework 1: The art and language of proof.
- Homework 2: More introductory proofs.
- Homework 3: Proof techniques; cardinality.
- Homework 4: More cardinality problems.
- Homework 5: Yet more cardinality problems.
- Homework 6: Set theory.
- Homework 7: More set theory.
- Homework 8: Yet more set theory.
- Homework 9: Equivalence relations.
- Homework 10: Revisions.
- Homework 11: Measures of sets.
- Homework 12: Sequences and limits.
- Homework 13: More limits.
- Homework 14: Review!
- Homework 15: Transcendental numbers (extra credit!)
- Homework 16: Linear algebra.
- Homework 17: Complex numbers.
- Homework 18: More complex numbers.