**Instructor:** Hemanshu Kaul

**Office:** 125C, Engineering 1

**Phone:** (312) 567-3128

**E-mail:** kaul [at] iit.edu

**Time:** 11:25am, Tuesday & Thursday.

**Place:** 119, Engg. 1 Bldg. for lectures; and 112F, Stuart Bldg. for labs.

**Office Hours:** 3:15-4:15pm Tuesday and Thursday, and by appointment.

Emailed questions are also encouraged.

**Recommended TA Office Hours:** Chris Mitillos, at 1:30pm-4:30pm Monday, 129, E1 Building.

The

The official course syllabi.

How to read Mathematics? The Basics, More Details.

How to study and learn Math.

Understanding Mathematics - a study guide

On a more abstract note, here is a discussion of Language and Grammar of Mathematics - which is what you are starting to learn in a course like this.

Excellent advice for math majors, especially those planning to go on to graduate school, by Terry Tao, 2006 Fields medallist. Required reading.

*Tuesday, 11/4*: See below for the slides and Matlab/Mathematica codes for special lectures.*Tuesday, 8/26*: Check this webpage regularly for homework assignments, announcements, etc.

The project requires you to work in teams of 2-3 students with the Professor offering the project. The project adviser will specify the details of what his/her project entails, the outlines are given in the descriptions below.

The successful completion of the project entails:

Before the project Starts -

1) Send me an email with your choice of project(s) by Wednesday, 9/24. Projects will be assigned in first-come first-serve order.

2) After I confirm your project and team members on Thursday, 9/25, set up an appointment via email with your chosen project adviser before Fri, 9/26 .

After the project starts -

3) Regular meetings with the project adviser and following his instructions.

4) A midterm report on the status of the project as required by the faculty adviser.

5) A final meeting with project adviser before Wednesday, 12/3 to confirm the completion of the project, and discuss the outcome of the project.

6) Submission of project report before the project presentation during Final exam week.

7) Final project presentation in front of your classmates during Final exam week.

**Project Option #1 :**Contact: Prof. Fred Hickernell.**Project Option #2 :**Contact: Prof. Shuwang Li.**Project Option #3 :**Contact: Prof. Lulu Kang.**Project Option #4 :**Contact: Prof. Hemanshu Kaul

**Homework #1 :**Due Thursday, 8/28

Read Preface, Introduction, and Chapter 1 of Introduction to Mathematical Thinking, by Keith Devlin, and be prepared for discussion in class.**Homework #2 :**Due Thursday, 9/4.

1) Write a 500-800 word paper comparing job profiles of two "mathematicians" (Here mathematician includes anyone who uses mathematics in their profession, not just professors/researchers and such). Your paper should:

- Be based on at least two different sources, preferably three or more;

- Compare/contrast such things as: required training (e.g., level of education, special courses inside or outside university, etc); job characteristics (e.g., field of work, specific responsibilities, etc.); salary, job satisfaction, quality of life, and/or; job outlook (available positions, changes to the profession, etc.)

- Have a clear structure (e.g., intro, body, conclusion);

- Include facts from the sources as well as your personal conclusions/opinions;

- Be concise (not rambling) and proofread for spelling, grammar, and flow;

- Reference all sources from which sections of text are copied or paraphrased. This is IMPORTANT to avoid plagiarism!

Citation format: Use what you prefer, so long as you include all necessary information to look up what you cite.

2) Write a roughly 500 word essay describing the life and mathematical contributions of your favorite Mathematician in history. The same rules as above apply to this essay as well: clear structure, facts as well as your own conlucsions/opinions, concise, references, etc.

**Homework #3 :**Due Thursday 9/11.

Read Chapter 2 of Devlin's textbook along with the lectures and be ready for discussion in class.**Homework #4 :**Due Tuesday 9/23.

1) Watch the videos:

MATLAB Intro 1

MATLAB Intro 2

MATLAB Intro 3

2) Read Preface and Chapter 1 of Moler's Experiments with MATLAB

3) Be ready to work with MATLAB in the lab on Tuesday, 9/23.

**Homework #5 [Part 1]:**Due Thursday 10/2.

Solve the following problems from the Devlin's textbook and submit the carefully written solutions in class:

Exercises 2.1.1: #6; Exercises 2.2.1: #2bdef, #4; Exercises 2.2.2: #1abd, #3; Exercises 2.2.3: #5ab; Exercises 2.3.3: #1bch, #2ade, #3, #5.

**Homework #5 [Part 2]:**Due Thursday 10/9.

Solve the following problems from the Devlin's textbook and submit the carefully written solutions in class:

Exercises 2.3.5: #3, #4, #5, #13, #14; Exercises 2.4.2: #4bde, #6; Exercises 2.4.5: #2dehin, #5bc.

**Homework #6 :**Due Friday 9/26, 11pm by email.

Solve the following problems from the Chapter 1 of Moler's Experiments with MATLAB and submit the combined solutions in one .m file through email to me:

1.2, 1.3, 1.4, 1.6, 1.7, 1.8, 1.10, 1.11, 1.13.**Homework #7 :**Due Friday 10/10, 11pm by email.

Solve the following problems from the Chapter 2 of Moler's Experiments with MATLAB and submit the combined solutions in one .m file through email to me:

2.3, 2.4, 2.6, 2.9.**Homework #8 :**Due Friday 10/17, 11pm by email.

Read Chapter 3 and solve the following problems from the Chapter 4 of Moler's Experiments with MATLAB and submit the combined solutions in one .m file through email to me:

4.3 (Show computation for specific examples and write out general form in comments), 4.4 (Show computation for specific examples and write out general form in comments), 4.5, 4.6, 4.7 (Do example computations for each item with example choices for the angle theta. Write an explanation in comments.), 4.10 (Do example computations for (a) and (b), and example animation for wiggle versus your customized wiggle for (c)).**Homework #9 [Part 1]:**Due Thursday 11/6.

Solve the following problems from the Devlin's textbook and submit the carefully written solutions in class:

Exercises 3.2.1: #1(but replace 3 by - show sqrt(5) is irrational); Exercises 3.3.1: #1, #2, #3, #4; Exercises 3.3.2: #3, #4g, #5g, #6c.**Homework #9 [Part 2] :**Due Thursday 11/13.

Solve the following problems from the Devlin's textbook and submit the carefully written solutions in class:

Exercises 3.4.1: #3, #4be; Exercises 3.5.2: #1, #3b.**Homework #10 :**Due Thursday 11/20, in class.

The**Scavenger Hunt Mystery term**as assigned to you by email.

Find a faculty member (including senior lecturers) who can explain to you the meaning of your "mystery term" and then write a short 2-3 paragraph (250-500 words) description of this topic that is suitable for publication on our department website or newsletter.

Here is an example published in IIT Applied Math's Fall 2011 newsletter:

Fall 2011 Newsletter

Look in the 3rd page

These are some**additional rules**for this assignment:

1) You must get your information from a real person in the department. You are supposed to meet people. Do not look up the terms on the internet or in a book.

2)**Provide "proof" of having consulted a "live" source by having that person sign your description.**

3) It may be difficult to find the "right" person to answer your question. Ask around, and try at least two different graduate students and two professors. (This means try asking two people first before asking me for help locating the person who knows the answer.) If by then you are still clueless, come to me and I will point you in the "right" direction.

4) Insist on an explanation that you can understand. Don't be afraid to ask questions. No one expects you to know any of this. In fact, you will probably learn that even graduate students and professors might not know (see "rule" #3).

5)**Go back and discuss your first write-up with the person who gave you the answer; ask followup questions to improve it.**

6) Add an illustrative picture if appropriate.

Moler's Experiments with MATLAB

Stuart Bldg Room 112 E,F

Tech North Room 110

Siegel Hall Room 237

- Matlab quick reference sheets, by Computer Integrated Systems for Microscopy and Manipulation, UNC.
- Getting Started in MATLAB (pdf) (some very basic info to get you off the ground)
- The MathWorks Student Center (all sorts of useful information)
- A Very Elementary MATLAB Tutorial from The MathWorks
- MATLAB 7: Getting Started Guide (should also be available directly through your MATLAB installation)
- Numerical Computing with MATLAB (by Cleve Moler). Probably, all you might need is the Introduction (pdf)
- Learning MATLAB (link to an intro text written by Toby Driscoll)
- MATLAB Webinar: Intro to MATLAB (you might need to register for this, but it's free)
- Official MATLAB Site
- Octave and Scilab, two inexpensive (FREE) alternatives to MATLAB

*Undergraduate studies in Applied Math - During and Afterwards*: Careers - Documentary, discussions, presentations by instructor and by Career Management Center. Managing Courses, how to study, and making the jump from High School Math to Undergrad Math.*Mathematical Statements and Logic*: Second order logic and simple mathematical statements, Comparison of Existential and Universal statements, the conjunction, disjunction, and their negations. Comparing Mathematical statements to real-life statements. Understanding Mathematical definitions and Statements of Theorems.*Mathematical Proofs*: Classical examples of proofs (non-proofs) from Geometry, Number Theory, Set Theory. Different types of proofs and how to find them and how to write them - Direct implications, Contradiction, Contrapositive, Mathematical Induction.*MatLab*: How to use Matlab to learn experimentation and computation in Mathematics - Fibonacci Sequence, Matrices, etc.*Special Lectures*: Lectures by faculty in Applied Math introducing different fields/topics within Applied Math and their connection to real-world, further courses in the curriculum.*Project*: A semester-long group project on investigation of a mathematical topic.*Scavenger Hunt*: Meeting faculty and learning through discussion.

*10/9*: Celestine McGee, Asst. Director, Career Management Center, will speak on Career opportunities for Applied Math majors.*10/28*: Prof. Igor Cialenco, Applied Math, will speak on Randomness and Probability.*10/30*: Prof. Lulu Kang, Applied Math, will speak on Statistics.*11/4*: Prof. Greg Fasshauer, Applied Math, will speak on Approximation and Computation. Here are the three Matlab/Mathematica code files used in the lecture - Asymptotic Solution for Quadratic Equation; Prime Number Theorem; Derivative Approximation*11/6*: Prof. Xiaofan Li, Applied Math, will speak on Applied Analysis - Fixed Point Theorems.*11/13*: Prof. Sonja Petrovic, Applied Math, will speak on Applied Algebra.*11/18 and 11/20*: Prof. Michael Pelsmajer, Applied Math, will speak on Graph Theory and Combinatorics.