# Dr. J. Ramanathan

### Mathematical Reasoning (Math 110)

#### Log

##### 16-04-2018 Mon

The key to quiz D is available.

##### 12-04-2018 Thu

A study guide to help you prepare for the final is available.

The final for the MW 12:30 pm section is scheduled for

• Wednesday, 18 April from 11:30 am to 1:00 pm.

The final for the MW 11:00 am section is scheduled for

• Monday, 23 April from 11:00 am to 12:30 pm.

(You must attend the exam that is scheduled for your class.)

##### 04-04-2018 Wed

There will be a group quiz on Monday, 9 April. The quiz will cover sections 5.1 - 5.3, 5.5-5.6.

You should be reading sections 5.6 and 5.7. The suggested problems for those sections are:

• Section 5.6: Exercises 1 - 24, odd.
• Section 5.7: Exercises 1 - 24, odd.
##### 02-04-2018 Mon

The final project, which is due on 11 April, has been posted. The role of this project will be discussed today.

##### 28-03-2018 Tue

Problem set X is the extra credit problem discussed in class yesterday. Please turn this in next Monday. Your write up should be on a separate sheet, i.e. not included with problem set G.

##### 26-03-2018 Mon

You should be reading sections 5.3 and 5.5. Suggested problems for these two sections are:

• Section 5.3: Exercises 1-28, odd.
• Section 5.5: Exercises 1-28, odd.

Problem set G is posted and had a due date of 2 April.

##### 19-03-2018 Mon

The key to problem set F is available.

##### 15-03-2018 Thu

A study guide to help you prepare for the test next week has been posted. There is no key for the practice problems. If you need hints please ask me on Monday in class or in office hours.

##### 14-03-2018 Wed

Problem set E is posted and is due 19 March. Read section 5.2. Suggested problems are:

• Section 5.2: Exercises 1 - 33, odd.
• Section 5.3: Exercises 1 - 28, odd.

The key to problem set E is posted.

##### 08-03-2018 Thu

I know I was supposed to post the next problem set. However, the performance in the last one looks quite bad. So, I will be returning it to you on Monday - ungraded. We will have a chat about the issues involved and you will have to do it over again for Wednesday. In the meantime, it is critical that you read the first four sections of chapter 4 very carefully. Look over the problems again and formulate questions for me on Monday.

##### 06-03-2018 Wed

The key to quiz C has been posted. Read section 5.2.

##### 28-02-2018 Wed

The key to problem set D is available.

##### 27-02-2018 Tue

Problem set E is posted and is due on 7 March. Read section 4.4. Suggested problems are

• Section 4.2: Exercises 1-23, odd.
• Section 4.3: Exercises 1-23, odd.
• Section 4.4: Exercises 1-23, odd.
##### 14-02-2018 Wed

The key to test 1 has been posted. Also, a small error in problem set D has been corrected.

##### 13-02-2018 Tue

Problem set D is posted and is due 26 February.

##### 02-02-2018 Fri

A study guide is available with practice problems to help you prepare for the test has been posted. I may add a few more problems, so please check back in over the next few days.

##### 29-01-2018 Mon

The key to problem set C is posted. Read section 3.5. There is a quiz Wednesday that will cover everything we have done to date from chapters 2 and 3.

##### 24-01-2018 Wed

The key to quiz A is posted. Read sections 3.3 and 3.4. The suggested problems from those two sections are

• Section 3.3: Exercises 1-24, odd.
• Section 3.4: Exercises 1-22, odd.
##### 21-01-2018 Sun

Read sections 3.1 and 3.2. Suggested problems from these two sections are

• Section 3.1: Exercises 1-24, odd.
• Section 3.2: Exercises 1-34, odd.

Problem set C is posted and is due on 29 January.

##### 18-01-2018 Thu

The group quiz on Monday will cover the first four sections of chapter 2. In preparation, you should:

• work on as many of the suggested problems (listed below) as you can.

The key to problem set B is available.

##### 17-01-2018 Wed

My office hours for this semester are:

• MW 10:30 - 10:55 am
• MW 1:45 - 2:30 pm
• MW 4:45 - 5:25 pm
##### 14-01-2018 Sun

The key to problem set A is available.

##### 10-01-2018 Wed

Problem set B is posted and is due next Wednesday, 17 January.

You should be reading 2.3 and 2.4. Here are some suggested problems from those sections:

• Section 2.3: Exercises 7-46, odd.
• Section 2.4: Exercises 5-32, odd.
##### 08-01-2018 Mon

You should be reading sections 2.2 and 2.3. Here are some suggested problems:

• Section 2.1: Exercises 9-30, odd.
• Section 2.2: Exercises 9-36, odd.
##### 08-01-2018 Mon

There seems to be a problem at the bookstore re the text. I am posting the first problem set with problems attached, so that students without the text can get the homework done this Wednesday.

##### 02-01-2018 Tue

The first reading assignment is to read sections 2.1 and 2.2 of the course pack. The first problem set is also available. The due date for me is Wednesday, 10 January.

##### 02-01-2018 Tue

The course syllabus has been posted.

The dates for the two tests are in that document. The dates for the final in my two sections of 110 are:

• MW 11:00 am section: Monday, 23 April 11:00 am - 12:30 pm
• MW 12:30 pm section: Wednesday, 18 April 11:30 am - 1:00 pm

### Mathematical Structures for Computer Science (Math 205)

#### Log

##### 04-16-2018 Mon

The final is one week from today (23 April) at the usual class time.

Slides that contain a few resources for further study are available.

Finally, the key to quiz C is available.

##### 04-15-2018 Sun

A set of practice problems has been posted to help you prepare for the final.

##### 04-04-2018 Wed

Read section 4.4 and skim 4.5 and 4.6. The suggested problems are

• Section 4.4: Exercises 1-12, odd, 31-39 odd.

There will be a group quiz on Monday on the first four sections of chapter 4.

Finally, a rough key to problem set G is available.

##### 26-3-2018 Mon

Problem set G is available. It is an extra credit assignment with your score being added directly to your score on test 2.

You should be reading chapter 4, sections 1-3. Suggested problems are listed in a previous post.

##### 19-03-2018 Mon

The key to problem set F is available.

Couple of code snippets have been uploaded as well. One is for calculating expansions of integers relative to any base. The other is for fast modular exponentiation.

##### 16-03-2018 Sat

A set of practice problems has been uploaded to help you with the upcoming test. The document also has a topic outline. This document may be updated a bit on Monday.

##### 14-03-2018 Wed

Read sections 4.1, 4.2 and 4.3. Suggested problems are:

• Section 4.1: Exercises 1 - 33, odd.
• Section 4.2: Exercises 1 - 28, odd.
• Section 4.3: Exercises 1 - 35, odd.

Problem set F is posted and is due 19 March. The key to problem set E is also available.

##### 07-03-2018 Wed

The key to problem set D has been posted. Read sections 3.1 and 3.2. I’m postponing the due date for problem set E to Monday.

##### 26-02-2018 Mon

If you got 32 or more points taken off on the test, you can submit solution to all the problems on the test to raise your score. I will grade this submission and rescale it so that the maximum possible is the difference between 60(= 92-32) and your score. That will be added to your score. This is due to me before class time next Monday. You can turn it in to the math department office or slip it under my door any time before the deadline.

##### 13-02-2018 Tue

Problem set D is posted and is due 28 February.

Read section 2.4 and 3.2 over break. Here are some suggested problems from these sections:

• Section 2.4: Exercises 1-26 odd, 29-37 odd.
• Section 3.2: Exercises 1-30 odd.
##### 08-02-2018 Thu

I have posted quiz B that we went over yesterday. An incorrect link below (to the practice problems) has also been corrected.

##### 07-02-2018 Wed

Read sections 2.5. Here are some suggested problems from sections 2.3 and 2.5:

• Section 2.3: Exercises 1-36, odd.
• Section 2.5: Exercises 1-17, odd.
##### 04-01-2018 Sun

A set of practice problems to help you prepare for the final is available.

##### 29-01-2018 Mon

The key to the first quiz is posted.

##### 24-01-2018 Wed

The keys to problem sets A and B are available above. Read sections 2.1, 2.2 and 2.3. The suggested problems are:

• Section 2.1: Exercises 1-44, odd.
• Section 2.2: Exercises 1-31, odd.
##### 21-01-2018 Sun

Problem set C is posted and is due 29 January. The little code snippet we discussed last Wednesday is available, as well.

##### 17-01-2018 Wed

The slides for the python introduction are posted.

##### 11-01-2018 Thu

My office hours for this semester are:

• MW 10:30 - 10:55 am
• MW 1:45 - 2:30 pm
• MW 4:45 - 5:25 pm
##### 10-01-2018 Wed

Problem set B is posted and is due Monday, 22 January.

Read chapter 1, sections 5 and 6. Suggested problems are

• Chapter 1, section 5: Exercises 1-40, every other odd.
• Chapter 1, section 6, Exercises 1-20, odd.
##### 08-01-2018 Mon

Here are some more suggested problems:

• Chapter 1, section 3: Exercises 1-33, odd.
• Chapter 1, section 4: Exercises 1-20,odd.
##### 03-01-2018 Wed

The reading assignment is chapter 1, sections 1,3 and 4. Suggested problems are

• Chapter 1, section 1: Exercises 31-41.
##### 02-01-2018 Tue

The syllabus for the course is available. The first problem set is also available. The due date for this problem set is Wednesday, 10 January.

### Books

##### Analysis
• Bressoud, David. A Radical Approach to Real Analysis. Mathematical Association of America, Washington D.C. 1994.

A genetic development of the basic notions of convergence.

• Courant, Richard and Fritz, John. Introduction to Calculus and Analysis I. Springer 1998.

A reissue of one of the classic calculus texts.

• Steele, Michael. The Cauchy-Schwarz Master Class. Cambridge University Press, New York 2004.

An engaging introduction to inequalities.

##### Biography
• Hoffman, Paul. The Man Who Loved Only Numbers. Hyerpion, New York 1998.

• Nasar, Sylvia. Beautiful Mind. Simon and Schuster, New York 1998.

##### Combinatorics
• Wilf, Herbert. Generating Functionology, 3rd ed.. Academic Press 1994.

Treats the application of power series to combinatorial problems. The second edition of the book in pdf format is available for free at: http://www.math.upenn.edu/~wilf/DownldGF.html.

• Conway, J.H. and Guy, R.K.. Book of Numbers. Copernicus, 1996.

Discusses the many amazing properties of the integers and integer sequences. Graphics in this book is striking.

##### Number Theory
• Apostol, T.M.. Introduction to Analytic Number Theory. Springer-Verlag 1976.

##### Physics
• Oliver, David. The Shaggy Steed of Physics, 2nd ed.. Springer, 2004.

A poetic book that uses the classical two-body problem to motivate many of the fundamental ideas in modern physics.

##### Probability
• Grimmett, G.R. and Stirzaker, D.R.. Probability and Random Processes. Oxford Univeristy Press, Oxford UK 2001.

Comprehensive introduction to probability good for upper level undergranduates and beginning graduate students.

• Klenke, A.. Probability Theory: A Comprehensive Course. Springer-Verlag, 2008.

This book is appropriate for a graduate student. It is very thorough and has non-trivial examples.

### Notes

##### Trigonometry in a Quick Turn

These notes cover elementary trigonometry from the unit circle point of view.

### Etceteras

#### 2017-06-01 Thu

Antarctic Ice Crack…

#### 2016-11-09 Wed

Field guide for the next four years … at least