Dr. Caldwell's Math 350 Syllabus

(This **Math 350** syllabus and other course resources are avaiable at **www.utm.edu/~caldwell**)

Dr. Caldwell, office 429 Humanities, office phone 7336. Department office 7360. E-mail: caldwell@utm.edu. Web page: www.utm.edu/staff/caldwell. I will use your e-mail as stored in Banner, usually an @ut.utm.edu account, to contact you (if the school closes, to send additional notes, ...) so please make sure that it is accurate.

**Math 350:** The integers: well-ordering, different bases, divisibility, primes, and factoring. The fundamental theorem of arithmetic and the division algorithm. Diophantine equations and applications of congruences. Pseudo-random numbers, pseudoprimes, and cryptography.

__ Friendly Introduction to Number Theory__, 4th Edition, Joseph H. Silverman.

We plan to cover the first 19 chapters and then continue based on student (and teacher) interests.

Students are encouraged to work together, but you must write up the solutions yourself, independently from others, while you are alone. I urge you to use the internet honestly. You may look up definitions but do not search for solution to the problems in assignments or ask about them on-line.

The library also has a great deal of useful books, many under the subject heading "elementary number theory." If you use ideas which are not your own, please indicate your source appropriately. If what you find makes the solution trivial, then check with me before submitting to make sure the abbreviated work will get full credit. The point of excises is to develop your understanding, not to borrow from others.

I assume you understand the university policies found in the student handbook.

Grading will be done according to the following weights in a "fair and subjective" manner

- 41% tests (approximately four one-hour tests)
- 29% homework (assigned daily)
- 19% final (comprehensive)
- 11% class project

When homework is assigned, I will tell you when it is due. Homework may be turned in early (place it in my mail box, my hand, or gently slide it under my door). Late homework will be reduced in value by 50% for each day, or fraction thereof, it is late. Some of the homework will be easy, some difficult and some may be impossible to fully complete--but you can show me what effort you made.

Upon completion of his/her degree from the University of Tennessee at Martin with a major in mathematics, the graduate will be able to:

- apply mathematical concepts and principles to perform numerical and symbolic computations;
- use technology appropriately to investigate and solve mathematical and statistical problems;
- write clear and precise proofs;
- communicate effectively in both written and oral form; and
- demonstrate the ability to read and learn mathematics and/or statistics independently.

The student will:

- Identify and apply various properties of and relating to the integers including the Well-Ordering Principle, primes, unique factorization, the division algorithm, and greatest common divisors.
- Identify certain number theoretic functions and their properties.
- Understand the concept of a congruence and use various results related to congruences including the Chinese Remainder Theorem. Solve certain types of Diophantine equations.
- Identify how number theory is related to and used in cryptography.

- The Prime Pages https://primes.utm.edu/
- Number Theory Web http://www.numbertheory.org/ntw/web.html
- MathSciNet Mathematical Reviews https://mathscinet.ams.org/mathscinet/search.html
- The On-Line Encyclopedia of Integer Sequences (OEIS) https://oeis.org/
- Prime Number Listening Guide https://primes.utm.edu/programs/music/listen/
- RSA FAQ http://www.nordugrid.org/documents/rsalabs_faq41.pdf

The Department of Mathematics and Statistics publishes a syllabus for each of it courses which may be viewed in my office or on the departmental web pages.

You (and the state) have paid well for the courses taught here so mathematics and statistics teachers very (very) rarely cancel classes. However, sometimes (especially in the spring) the university closes due to bad weather. If this happens, I will contact you *by the e-mail address* *stored in the Banner system* to let you know how we will make up the work. I will also adjust the homework schedule on-line as needed.

The University of Tennessee provides reasonable accommodations (academic adjustments and auxiliary aids) to ensure equal access to educational content and university programs for students with disabilities. Students who are eligible for and who request accommodations through the Disability Services office must provide instructors with a letter of accommodation. The Disability Services office is located in the Student Success Center, 209 Clement Hall, (731) 881-7605.

- Ask in class.
- Study with a friend.
- Form a study group in the class
**Drop by my office**(office hours are posted on my homepage; but I am avaiable at many other times as well!)