Info Page

MAT 513 Spring 2021 Course Information

Announcements are posted below the course schedule. Most recent announcements at the top.

Tentative Schedule

Mon 2/1 1. Snow Day Watch the snow fall.

Wed 2/3 2. Introduction. Read sections 1.1 - 1.2

Mon 2/8 3. Completeness Axiom, Archimedean Property Read sections 1.3 - 1.4

Wed 2/10 4. Cardinality, Cantor's Theorem Read sections 1.5 - 1.7

Mon 2/15 5. Supremum, infimum. Why convergence matters. Read sections 2.1 - 2.2. Homework 1 Due Today

Wed 2/17 6. Limit of a sequence, Some limit theorems. Read sections 2.3 - 2.4

Mon 2/22 7. Monotone Convergence Theorem, HW 1 Discussion Read sections 2.5 Homework 2 Due Today

Wed 2/24 8. Subsequences, Bolzano-Weierstrass, Cauchy Criterion Read sections 2.6

Mon 3/1 9. Convergence of series Read sections 2.7-2.9

Wed 3/3 10. Topology of Real line: Open sets, Closed sets, Density of Q in R Read sections 3.1 - 3.2 Homework 3 Due Today

Mon 3/8 11. Compact sets, connected sets. Read sections 3.3 - 3.4

Wed 3/10 12. EXAM 1: Covers in-class material and reading through March 3.

Mon 3/15 13. More point set topology. Compact sets

Wed 3/17 14. Heine-Borel Theorem, connected sets, Cantor set Take home component of Exam 1 Due Today.

Mon 3/22 15. Limit of a function, Sequential criterion Read sections 4.1 and 4.2

Wed 3/24 16. Continuity, Continuous functions on compact sets Read sections 4.3 and 4.4 Homework 4 Due Today

Mon 3/29 17. WE WILL NOT MEET IN CLASS TODAY MATERIAL TO BE POSTED ON-LINE

Wed 3/31 18. Uniform continuity, Intermediate Value Theorem Read through at least 4.5

Mon 4/5 19. Derivatives Read sections 5.1, 5.2 Homework 5 Due Today

Wed 4/7 20. Darboux's Theorem Read sections 5.3, 5.4

Mon 4/12 21. Mean Value Theorem

Wed 4/14 22. L'Hospital's Rule Homework 6 Due Today

Mon 4/19 23. EXAM 2:

Wed 4/21 24. Integration

Mon 4/26 25.

Wed 4/28 26.

Mon 5/3 27.

Wed 5/5 28.

Tue 5/18 FINAL EXAM Final Exam

ANNOUNCEMENTS:

March 15: The schedule above was updated today. Please note: we will not meet in-class on Monday, March 29. I will post material for you to access according to your schedule.

February 22: The schedule above was updated today.

February 7: The schedule above was updated today.

Mon 2/1	1.	Snow Day	Watch the snow fall.
Wed 2/3	2.	Introduction.	Read sections 1.1 - 1.2
Mon 2/8	3.	Completeness Axiom, Archimedean Property	Read sections 1.3 - 1.4
Wed 2/10	4.	Cardinality, Cantor's Theorem	Read sections 1.5 - 1.7
Mon 2/15	5.	Supremum, infimum. Why convergence matters.	Read sections 2.1 - 2.2. Homework 1 Due Today
Wed 2/17	6.	Limit of a sequence, Some limit theorems.	Read sections 2.3 - 2.4
Mon 2/22	7.	Monotone Convergence Theorem, HW 1 Discussion	Read sections 2.5 Homework 2 Due Today
Wed 2/24	8.	Subsequences, Bolzano-Weierstrass, Cauchy Criterion	Read sections 2.6
Mon 3/1	9.	Convergence of series	Read sections 2.7-2.9
Wed 3/3	10.	Topology of Real line: Open sets, Closed sets, Density of Q in R	Read sections 3.1 - 3.2 Homework 3 Due Today
Mon 3/8	11.	Compact sets, connected sets.	Read sections 3.3 - 3.4
Wed 3/10	12.	EXAM 1: Covers in-class material and reading through March 3.
Mon 3/15	13.	More point set topology. Compact sets
Wed 3/17	14.	Heine-Borel Theorem, connected sets, Cantor set	Take home component of Exam 1 Due Today.
Mon 3/22	15.	Limit of a function, Sequential criterion	Read sections 4.1 and 4.2
Wed 3/24	16.	Continuity, Continuous functions on compact sets	Read sections 4.3 and 4.4 Homework 4 Due Today
Mon 3/29	17.	WE WILL NOT MEET IN CLASS TODAY	MATERIAL TO BE POSTED ON-LINE
Wed 3/31	18.	Uniform continuity, Intermediate Value Theorem	Read through at least 4.5
Mon 4/5	19.	Derivatives	Read sections 5.1, 5.2 Homework 5 Due Today
Wed 4/7	20.	Darboux's Theorem	Read sections 5.3, 5.4
Mon 4/12	21.	Mean Value Theorem
Wed 4/14	22.	L'Hospital's Rule	Homework 6 Due Today
Mon 4/19	23.	EXAM 2:
Wed 4/21	24.	Integration
Mon 4/26	25.
Wed 4/28	26.
Mon 5/3	27.
Wed 5/5	28.
Tue 5/18		FINAL EXAM	Final Exam