2023 Fall Course Syllabus - Mathematics 3003.001

Course: Mathematics 3003.001.

Course Title: Theory of Numbers.

Credits: 3.

How this course will be taught: In Person.

Time: MWF 14:00-14:50.

Place: Wachman 408.

Instructor: Charles Osborne.

Instructor Office: Wachman 1035.

Instructor Email: charles.osborne@temple.edu

Instructor Phone: 609 634 4080.

Office Hours: M 9:50 - 10:50, WF 10:50-11:50, and by appointment.

Prerequisites: A grade of C or better in Math 2111, or equivalent transfer credit.

Course Materials: Our course textbook will be Elementary Number Theory (6th Edition), by Kenneth H. Rosen.

Course Goals: To study the divisibility properties of integers, prime factorization, distribution of primes, linear and quadratic congruences, primitive roots, quadratic residues, quadratic reciprocity, simple Diophantine equations, cryptology.

Topics Covered: We plan to cover the following sections of the book: 1.1, 1.5, 3.1-3.5, 3.7, 4.1-4.3, 5.1, 6.1, 6.3, 7.1, 8.1-8.4, 7.2, 7.4, and 9.1-9.3 Chapter 1: The Integers 1.1: Numbers and Sequences 1.5: Divisibility Chapter 3: Primes and Greatest Common Divisors 3.1: Prime Numbers 3.2: The Distribution of Primes 3.3: Greatest Common Divisors and their Properties 3.4: The Euclidean Algorithm 3.5: The Fundamental Theorem of Arithmetic 3.7: Linear Diophantine Equations Chapter 4: Congruences 4.1: Introduction to Congruences 4.2: Linear Congruences 4.3: The Chinese Remainder Theorem Chapter 5: Applications 5.1: Divisibility Tests Chapter 6: Some Special Congruences 6.1: Wilson's Theorem and Fermat's Little Theorem 6.3: Euler's Theorem Chapter 7: Multiplicative Functions 7.1: The Euler Phi-Function Chapter 8: Cryptology 8.1: Character Ciphers 8.2: Block and Stream Ciphers 8.3: Exponentiation Ciphers 8.4: Public Key Cryptography Chapter 9: Primitive Roots 9.1: The Order of an Integer and Primitive Roots 9.2: Primitive Roots for Primes 9.3: The Existence of Primitive Roots.

Course Grading: The grade will be based on two midterms, one final exam, and submitted homework. Grades will be computed in a straightforward manner, dividing points earned by possible points. Course averages correspond to letter grades as follows: 0-49 F, 50-54 D-, 55-64 D, 65-69 D+, 70-72 C-, 73-76 C, 77-79 C+, 80-82 B-, 83-86 B, 87-89 B+, 90-92 A-, 93-100 A.

Exam Dates: Midterms will occur at the beginning of October and the middle of November; exact dates will be announced in class. Both midterms will be held during regular course hours.

Attendance Policy: Attendance is required. Students who miss 4-7 classes without a documented excuse, will have their grades lowered by one notch (e.g., from C to C-); who miss 8-11 classes, will have their grades lowered by two notches, etc.

Attendance and Your Health: To achieve course learning goals, students must attend and participate in classes, according to your instructors' requirements. However, if you feel unwell or if you are under quarantine or in isolation because you have been exposed to the virus or tested positive for it, you should not come to campus or attend in-person classes or activities. Students have the responsibility to contact their instructors to create a plan for participation and engagement in the course as soon as they are able to do so and to make a plan to complete all assignments in a timely fashion when illness delays their completion.

Homework: Homework will be assigned at the end of every class, but not all of it will be collected. Instead, every Friday (with the exception of the first Friday of the class and exam dates), I will indicate which of the assigned problems will be collected. These are due the subsequent Friday.

Calculator Policy: No calculators are allowed in class or on the tests.

Make Up Tests: Make up tests will only be given in cases of documented emergencies. A student cannot make up a test after the graded test was returned. You must contact me by e-mail as soon as possible in case of a missed test. Tardiness in doing so may result in your not being able to make up the test even if you have a legitimate reason for missing it.

Disability Statement: Any student who has a need for accommodations based on the impact of a documented disability or medical condition should contact Disability Resources and Services (DRS) in Howard Gittis Student Center South, Rm 420 (drs@temple.edu; 215-204-1280) to request accommodations and learn more about the resources available to you. If you have a DRS accommodation letter to share with me, or you would like to discuss your accommodations, please contact me as soon as practical. I will work with you and with DRS to coordinate reasonable accommodations for all students with documented disabilities. All discussions related to your accommodations will be confidential.

Academic Freedom: Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here (opens in new tab/window).

Add/Drop Policy: Students will be charged for a course unless dropped by the Drop/Add deadline date. Check the University calendar (opens in new tab/window) for exact dates.

During the Drop/Add period, students may drop a course with no record of the class appearing on their transcript. Students are not financially responsible for any courses dropped during this period. In the following weeks prior to or on the withdrawal date students may withdraw from a course with the grade of "W" appearing on their transcript. After the withdrawal date students may not withdraw from courses. Check the University Calendar (opens in new tab/window) for exact dates. See the full policy by clicking here (opens in new tab/window).

Incomplete Policy: The grade "I" (an "incomplete") is only given if students cannot complete the course work due to circumstances beyond their control. It is necessary for the student to have completed the majority of the course work with a passing average and to sign an incomplete contract which clearly states what is left for the student to do and the deadline by which the work must be completed. The incomplete contract must also include a default grade that will be used in case the "I" grade is not resolved by the agreed deadline. See the full policy by clicking here (opens in new tab/window).

Student Support Services: The following academic support services are available to students (all links open in a new tab/window):
    The Math Consulting Center
    Student Success Center
    University Libraries
    Undergraduate Research Support
    Career Center
    Tuttleman Counseling Services
    Disability Resources and Services
If you are experiencing food insecurity or financial struggles, Temple provides resources and support. Notably, the Temple University Cherry Pantry and the Temple University Emergency Student Aid Program are in operation as well as a variety of resources from the Division of Student Affairs.