# Number Theory

### Course Details

This course is delivered by Westcott Courses in partnership with Brandman University

MATU 320 - Number Theory

Prerequisite: Methods of Proof and Linear Algebra with a grade of C or better.

Course Description: An introduction to the principles and concepts of Number Theory. Topics include distribution of primes, representations of integers, Fibonacci numbers, divisibility, Euclidean algorithm, fundamental theorem of arithmetic, number-theoretic functions, Diophantine equations, congruence, primitive roots, the Chinese remainder theorem, quadratic residues, and elementary partition theory. Note: This course is proof based and not digital. All homework assignments, exams and the final are graded by the instructor.

Enrollment Schedule: Enroll any day of the year, and start that same day. Students have five months of access, plus a 30 day extension at the end if needed. Students can finish the self-paced courses as soon as they are able. Most students finish the lower level courses in 4 - 8 weeks. The upper level math classes, such as Calculus and above, usually take students 3-4 months. (Note: The 30-day extension cannot take your total course time six months beyond the date of enrollment. At the end of the six months, we must post a grade with the university.)

### Duration

5 months to complete

Single 30 day extension if needed

### Estimated Cost

\$973

Payment Plan: First payment of \$538.65 and a second payment 30 days later of \$441.35.

Online

### Credit

Upper Division, UG

## Program Partner

We partnered with with Westcott Courses to offer online remedial, general education and other courses that count towards degree completion.

### Upon successful mastery of this course, you will be able to:

• Apply divisibility properties and the Fundamental Theorem of Arithmetic.
• Use the Euclidean algorithm to find the greatest common factor of two integers.
• Find integral solutions to specified linear Diophantine equations.
• Apply the Chinese remainder theorem.
• Solve systems of linear congruencies.
• Understand the basic properties of integers, including divisibility, primality, congruence, number theoretic functions, and their applications.
• Apply Fermat's Little theorem to prove relations involving prime numbers.
• Use Wilson's theorem to solve congruencies involving factorials.
• Apply the Mobius Inversion formula.
• Understand current unsolved problems about primes and their importance to the field of mathematics and other related fields.

Course Topics:

 Basis Representation The Fundamental Theorem of Arithmetic Combinatorial and Computational Number Theory Fundamentals of Congruences Solving Congruences Arithmetic Functions Primitive Roots Prime Numbers Quadratic Residues Sums of Squares Elementary Partition Theory Partition Generating Functions

#### Earn your credit in 4 simple steps

Step 1
Register and enroll in your course via Westcott Courses.

Step 2
Once you enroll, Westcott Courses will forward your registration to Brandman University.

Step 3
You will be working directly with Westcott Courses from the beginning to end of the course.

Step 4
Once your course is completed, your grade will be posted with Brandman University and you can then order a transcript.

Resources

Syllabus

## How it Works

These individual courses are available to anyone in the public who would like to enroll in a math or general education course. Unlike traditional colleges where one must enroll in a degree granting program, Westcott Courses offers individual courses where filling out a one page form makes the course immediately available. Westcott Courses is the teacher of the course and your official transcript with academic semester credits will come from one of our partner universities which are regionally accredited by WASC. Westcott Courses does not appear on the transcript; the transcript will show our courses the same way it would show a traditional class taken on the universities campus without being enrolled as a regular student. View transferring the credits.

Teachers for the Course

The classes are self-paced; however, a teacher is attached to each course who holds at least a master's degree in their field of study (or related). Most of our teachers are teachers who teach the exact same course on either a California State University or California Community college campus.

Omega MathTM Courses

Courses that have the trademark of "Omega MathTM Courses", are courses that have been written by our Omega Math team, and have a format that students love! These courses contain all the lessons, homework, solution manuals, quizzes, tests and the final. Students can take each test and quiz twice, and only the higher of the two scores counts towards their grade. This feature enables students to figure out what they did wrong before pushing forward, providing them with a deeper understanding of the course material.

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