**Teaching****
**

My teaching responsibilities for
2016-2017 are:

**Mathematics
419**/**Mathematics
545** Section 201 **Stochastic Processes/Probability II.**

Course outline.

Lemma 1.7

Notes on Conditional Expectation from 418/544 by Adrian She

Theorem 2.13

Lemma 2.23

Notes on Optional Sampling

Notes on Transience of 3-d SSRW

Uniqueness of Stationary Measures (Thm. 4.26)

Proof of Lemma 4.32 on aperiodic states

Exercise on using the MC Convergence Thm.--some hints

A Lemma for the Kolmogorov Continuity Theorem

Late assignments will not be accepted.

**Mathematics
418**/**Mathematics
544** Section 101 **Probability I.**

NEW: The midterm will be in Neville Scarfe Room 209 (SCRF209) 5:30-7:30 on Thurs. Nov. 17.

Practice Questions for Midterm

Solutions to Practice Questions for Midterm

Proof of Theorem 3.3 d) implies e)

Late assignments will not be accepted.

**Mathematics
320** Section 101 **Real Variables I.**

Course Outline (including grading system)

**Text:** The text for the course is Principles of Mathematical Analysis, 3rd
edition, Walter Rudin, McGraw-Hill. It is easy to find solutions to the
exercises in the text on the web--for example one set is at
https://minds.wisconsin.edu/handle/1793/67009
but we do not vouch for correctness of these or any other solutions.

With respect to Homework, sharing of ideas is fine but sharing of written solutions is not. Each homework will be announced and posted here at least a week in advance. The homeworks are due in class on the due date. If you cannot come to class, you may drop off your homework at your instructor's office on the day before it is due. Late assignments will not be accepted.

**Final Exam:** The final exam is Thurs. Dec. 8 from 8:30 to 11:00 am in
West Mall Swing Space 222. Old exams may be found at
Past exam database.
Here is a set of solutions for last years exam.

Office hours for the exam week are scheduled for Monday Dec. 5, 2-3:30 in my office (Math Annex 1207) and Wed. Dec. 7 10-11:30 in Irving Barber Learning Centre (IBLC) Room 461.

Homework 1

Solutions to Homework 1

Homework 2

Solutions to Homework 2

Homework 3

Solutions to Homework 3

Homework 4

Solutions to Homework 4

Homework 5

Solutions to Homework 5

Homework 6

Solutions to Homework 6

Homework 7

Solutions to Homework 7

Practice Test

Practice Test Solutions

Solutions to Practice Questions from Rudin Ch. 2

Test

Test Solutions

A Note about Least Upper Bounds

Proof of Schwarz Inequality for Complex Numbers

An inductively defined sequence

Appendix for Prop. 4.7 and 4.8

Connected subsets of the reals

Notes on Subsequences and Limsup

Uniform Continuity and Extension of Continuous Functions

**Additional resources:**

Past exam database

Curriculum
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