Theory of Numbers
3
In person
MWF 09:00 - 09:50
Wachman 15
Wachman 1035
609 634 4080
MWF 10:00 - 11:00, and by appointment
Our course textbook is Elementary Number Theory (6th Edition), by Kenneth H. Rosen.
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.
A grade of C or better in Math 2111, or equivalent transfer credit.
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.
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.
We will have two common midterms, and a final exam. Test 1 - Friday, 21 February (in class), Test 2 - Friday, 11 April (in class), Final Exam - Monday, 5 May, (08:00 - 10:00).
Attendance is required. Students who miss 6-11 classes without an excuse will have their grades lowered by one notch (e.g., from B to B-). Those who miss 12-17 classes ( without an excuse will have their grades lowered by two notches, etc.
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.
There will be no regularly scheduled make up exams. In the case of a DOCUMENTED EMERGENCY that prevents a student from taking a test as scheduled, the student must contact their professor, Charles Osborne at cosborne@temple.edu to share documentation and discuss alternative arrangements.
We have a zero tolerance policy towards cheating. Students caught cheating on a problem in a test (receiving outside help, using unauthorized resources or devices such as calculators, online resources, etc.) will receive a score of 0 for the entire test. This is consistent with the Temple University Academic Honor Code (see https://secretary.temple.edu/sites/secretary/files/policies/03.70.12.pdf ) that states: "Every member of the university community is responsible for upholding the highest standards of honesty at all times. Students, as members of the community, are responsible for adhering to the principles of academic honesty and integrity". More serious penalties are possible and those caught cheating will be reported to the office of student conduct.
This is a registered Canvas course. Please go there regularly to see important announcements and keep track of your current grades.
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.
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.
To achieve course learning goals, students must attend and participate in classes, according to the course requirements. However, if you have tested positive for or are experiencing symptoms of a contagious illness, you should not come to campus or attend in-person classes or activities. It is the student’s responsibility to contact me to create a plan for participation and engagement in the course as soon as you are able to do so, and to make a plan to complete all assignments in a timely fashion.
It is important to foster a respectful and productive learning environment that includes all students in our diverse community of learners. Our differences, some of which are outlined in the University's nondiscrimination statement, will add richness to this learning experience. Therefore, all opinions and experiences, no matter how different or controversial they may be perceived, must be respected in the tolerant spirit of academic discourse.
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.
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).
The use of generative AI tools (such as ChatGPT, DALL-E, etc.) is not permitted in this class unless specifically announced for a particular assignment; therefore, any use of AI tools for work in this class may be considered a violation of Temple University's Academic Honesty policy and Student Conduct Code, since the work is not your own. The use of unauthorized AI tools will result in a grade of zero on the assignment; a second offense will be reported to the Student Conduct Board.
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).
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).