Lecture Schedule / Homework Assignments
- Fri 12/6: Final Exam. 1-3pm in HA 425.
- Wed 12/4: Exam review. HW10 due.
- Mon 12/2: Ch 2.9. Series of real numbers and vectors.
- Wed 11/27: Thanksgiving Break.
- Mon 11/25: Ch 4.8. The Riemann integral.
- Wed 11/20: Ch 4.7 continued. Mean value theorem, Inverse function theorem. Introduction to the Riemann integral.
HW10 Due Wed 12/4.
- Mon 11/18: Ch 4.7. Differentiability.
Proof of the chain rule. This is a different proof than the one in the book.
- Wed 11/13: Ch 4.4, 4.5, 4.6. Boundedness of continuous functions on compact sets. The intermediate value theorem. Uniform continuity
HW9 Due Wed 11/20.
- Mon 11/11: Veterans Day no class.
- Wed 11/6: Ch 4.2, 4.3. Continuous maps and connected/compact sets; operations on continuous maps.
HW8 Due Wed 11/13.
- Mon 11/4: Ch 4.1. Continuous functions/maps. Update: Added a hint to Problem 4 in HW7.
- Wed 10/30: Ch 3.4, 3.5 Path connected and connected sets.
HW7 Due Wed 11/6.
Update 11/2: Typo fixed in Problem 5.
- Mon 10/28: Ch 3.1, 3.2, 3.3 Compact sets continued, the Heine-Borel theorem.
HW6 has been updated with an additional problem.
- Wed 10/23: Ch 3.1 Compact sets, the Bolzano-Weierstrass theorem.
HW6 Due Wed 10/30.
- Mon 10/21: Exam I in class.
- Wed 10/16: Review for midterm. HW5 due.
- Mon 10/14: Columbus Day no class.
- Wed 10/9: Ch (2.6), 2.7, 2.8. (Boundary of a set - mentioned last time, will be covered on 10/16) Sequences and completeness in metric spaces and R^n.
HW5 has been updated with additional problems.
Update 10/15: Problem 9 is a little challenging, but fun -- a hint: the maximum number is more than 12, but less than 20.
- Mon 10/7: Ch 2.2, 2.3, 2.4, 2.5. Interior of a set, closed sets, accumulation points, closure of a set.
Update: Homework 5 (will be) lengthened and the deadline extended: it will now be due Wednesday 10/16. Note that next Monday is a holiday.
- Wed 10/2: Ch 2.1,
2.2.Open sets, interior of a set.HW4 due in class.
HW5 (Updated 10/9) Due Wed
- Mon 9/30: Ch 1.7. Metrics, norms and inner products.
Update: There was a typo in Problem 4 of HW4 which has now been corrected.
- Wed 9/25: Ch 1.5, 1.6. liminf and limsup continued. Intro to Euclidean space.
HW3 due in class.
HW4 Due Wed 10/2.
- Mon 9/23: Ch 1.5. Cluster points, liminf and limsup.
- Wed 9/18: Ch 1.4. Cauchy sequences. HW2 due in class.
HW3 Due Wed 9/25.
- Mon 9/16: Ch 1.3. Least upper bounds.
Here is the proof that nth roots of positive elements exist in the real numbers that I gave in class. (Including the bit that I skipped after confusing myself!)
- Wed 9/11: Ch 1.2, pp. 39-45. Completeness and the real numbers. HW1 due in class.
HW2 Due Wed 9/18: p. 45: #1, 4. p. 97 #4, 5, 7.
- Mon 9/9: Ch 1.2, pp. 35-39. Sequences, limits and convergence.
- Wed 9/4: Ch 1.1. Ordered Fields.
HW Due Wed 9/11: Prove the rest of Proposition 1.1.2, p. 35: #5, p. 45: #2, #3. (The problems are typed up here in case you don't yet have the textbook.)
Here are some notes on induction and contradiction, including a proof of the well-ordering property of the natural numbers.