**Mathematical Explorations - Math 215 - Spring 2008**

**Lecturer:**- Irina Mitrea, 225 Kerchof Hall, im3p@virginia.edu, Phone: 982-2787.

**General description:***The course provides an introduction to the mathematical software Matlab and Mathematica while engaging the participants in the exploration of classical topics from calculus and introductory linear algebra, to the mathematics behind the secret codes; from prime numbers to exploring the periodicity in the Escher patterns. The course is restricted to second year students.*

**Prerequisite:**The course is appropriate for any student who has finished Math 122.

**Course web page:**-
http://www.people.virginia.edu/~im3p/mathpage215_2008.html

- MW 15:30- 16:45 p.m., BRN 203

- Irina Mitrea, 225 Kerchof Hall, Mondays and Wednesdays 12:00 noon - 1:00 pm (or by appointment).

**Examinations:**- Prelim 1: Wednesday, February 27th, 15:30-16:45 pm.
- Prelim 2: Wednesday, March 26th, 15:30-16:45 pm.
- Final Project Presentations: during lecture meetings -- exact dates TBA

**Topics Covered:**- Wednesday, January 16th: Overview; Can computers compute?
- Monday, January 21st: no class - Martin Luther King Day
- Wednesday, January 23rd: Rational numbers, prime numbers, Fermat numbers, proofs by induction, introduction to basic Matlab commands (part I)
- Monday, January 28th: class canceled
- Wednesday, January 30th: Fibonacci numbers and the Golden Ratio, introduction to basic Matlab commands (part 2)
- Monday, February 4th: Matlab - Lab 1
- Wednesday, February 6th: The Bisection Method for root finding problems, Matlab - Lab 2
- Monday, February 11th: Matrix manipulations, Matlab - Lab 3
- Wednesday, February 13th: Newton's Method for root finding problems, Matlab - Lab 4
- Monday, February 11th: Mathematics, why do it (overview of research and career opportunities in mathematics), Matlab - Lab 5
- Monday, February 25th: Making Matlab Animations, Matlab - Lab 6
- Wednesday, February 27th: Preliminary Examination 1.
- Monday, March 10th: Modular arithmetic: Caesar's Chipher and the Multiplication Cipher
- Wednesday, March 12th: Cryptanalysis for the Multiplication Cipher, Matlab - Lab 7
- Monday, March 17th: Introduction to the Multiplication-Shift Cipher, Matlab - Lab 8
- Wednesday, March 19th:
Introduction to the General Multiplication-Shift Cipher,
Matlab - Lab 9

**Grading:***Prelims count 25% each, the final project is worth 30% and the remaining 20% is for homework. 5% bonus points go towards outside class mathematical activities (e.g., UVa Undergraduate Mathematics Lecture Series, Mathematical Contest in Modeling Competition, Math Club).**A: 90-100**B: 80-89**C: 70-79**D: 60-69**F: <60*

**Homework**:*To be handed in during lecture meetings on the dates indicated in the homework outline. Do all problems assigned. These will be graded and returned to you the next week. Please be sure that your work is legible.***No late homework will be accepted.**You may work cooperatively on assignments provided- You write up the solution yourself.
- You put a note on your homework indicating the names of anyone you worked with.

**Incomplete**:*An incomplete will be given only in those rare circumstances where a student has completed all but a small portion of the course with a grade C or better and a severe, unexpected event prevents him/her from completing the course. In particular, if you get behind in the course you cannot ``bail out" by taking an incomplete.*

**Attendance and absences**:*You are responsible for the material covered in class, whether you attend or not. You are also responsible for the announcements made during class; these may include changes in the syllabus.*

**Academic honesty***is fundamental to the activities and principles of a University. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. When in doubt about plagiarism or collaboration, consult the course instructor. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion.*

**If you need accommodations because of a disability**,*if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please inform me immediately. Please see me after class, or at my office.*

**Words of advice:***I encourage you to ask questions about the HW.***Keep up with the latest materials covered**; experience shows that, otherwise, you are likely to get poor grades on the exams. If you miss a class, make sure you get the notes from someone else who attended it. The professor will not assist any absentee to find out what happened in his/her absence. Hard work and regular attendance will get you through this course.