Dr. J. Ramanathan


Mathematical Reasoning (Math 110)

Course Documents


19-10-2017 Thu

The key to problem set D and the key to the first test are available.

18-10-2017 Wed

Problem set E is posted and is due 24 October. You will need the excel data file called statePopulations.xlsx.

06-10-2017 Fri

Review problems A contains ten problems for you to work on in preparation for the midterm next Thursday. In addition to this, you should be going over the old problem sets and their keys. Working on the suggested problems listed in this log is also highly recommended.

03-10-2017 Tue

Key to problem set C is available.

Suggested problems for chapter 4 are:

  • Chapter 4: 4.7.13, 4.7.15, 4.7.16, 4.7.17, 4.7.18
  • Chapter 4: Review Exercises 4.7.25-26

A rough key for the quiz has been posted.

02-10-2017 Mon

Key to problem set B is posted. You should be reading chapters 4 and 5. Problem set D is posted and is due 10 October.

25-09-2017 Mon

Problem set C is posted and is due 3 October. You should be reading chapter 3 and working on the following suggested problems:

  • Chapter 3: 3.10.3, 3.10.13, 3.10.15, 3.10.21, 3.10.26
  • Chapter 3: Review Exercises 3.10.67-68
19-09-2017 Tue

The key to problem set A is posted.

15-09-2017 Fri

Couple of corrections: The first quiz will be next Thursday. Also, I’m moving the due date for problem set B to Tuesday, 26 September.

13-09-2017 Wed

The first quiz will be next Tuesday. It will consist of five problems modeled after the review exercises in chapter 1. Problem set B is posted and is due 21 September. Read chapter 2 of the text. Finally, the suggested problems are

  • Chapter 2: Exercises 2.9.2, 2.9.3, 2.9.12, 2.9.13, 2.9.18, 2.9.24
  • Chapter 2: Review Exercises 2.9.53-61
12-09-2017 Tue

I have written up couple of Fermi problems that we discussed in class last week as well as the suggested problem, exercise 1.8.3. These should serve as models for the problem set due Thursday. The document is linked here.

06-09-2017 Wed

Problem set A is posted and is due Thursday, 14 Sept.

Read chapter 1 of the text. Suggested problems are

  • Chapter 1: Exercises 1.8.3, 1.8.7, , 1.8.29, 1.8.32, 1.8.41
  • Chapter 1: Review Exercises 1.8.51-54
29-08-2017 Tue

The course syllabus has been posted.

The final exam dates and times for my two sections of Math 110 are listed below:

  • TR 3:30 pm section: 14 December, 3:00 - 4:15 pm
  • TR 5:30 pm section: 19 December, 5:30 - 6:45 pm

Field Theory (Math 514)

Course Documents


21-10-2017 Sat

Problem set F is posted. It contains some problems that might be useful in preparing for next weeks festivities. There is no due date.

18-10-2017 Wed

Review sheet A is an html document that contains the topic that will be covered in the midterm. Depending on how far we get, some of the items at the end might be modified.

15-10-2017 Sun

Problem set E is posted and is due on 24 October. Also, the date of the midterm has been postponed till 26 October.

05-10-2017 Thu

Problem Set D is posted with a due date of 12 October. Suggested problems B is also available.

02-10-2017 Mon

You should be reading sections 3 and 4 of chapter 3.

25-09-2017 Mon

Read chapter 2 and the first two sections of chapter 3. Problem Set C is posted with a due date 3 October.

13-09-2017 Wed

Problem set B is posted with a due date of 21 September.

12-09-2017 Tue

A set of slides for the ring theory review has been posted.

I will also be posting suggested problems throughout the semester. The first such is available. Please bear in mind that I may be adding some more problems to this document. Of course, I will announce any such additions here.

06-09-2017 Wed

A short set of slides summarizing the course syllabus is available.

We will begin with a review of group theory and ring theory. A set of slides for the group theory review has also been posted.

01-09-2017 Fri

The course syllabus and the first problem set are both available. The due date for problem set A is 14 September.

Finally, two very important pieces of information follow. The dates for the midterm and final are

  • Midterm: 19 October
  • Final: 19 December

Both exams will be given during the regular class time.


  • 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.

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

    About Paul Erdos.

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

    About John Nash.

  • 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.

    A comprehensive introduction to number theory aimed at advanced undergraduates and graduate students.

  • 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.

  • 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.


Trigonometry in a Quick Turn

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