MATH 307

 MERCY COLLEGE 

Department of Mathematics and Computer Science 

Number Theory Math 307 

Course Outline

Prof. Rafael Gonzalez

SCHEDULE: Math 307 Section DFA, Spring 2023, Thu 6:15-9:05PM, Online-Synchronous

WEBSITE: www.RafaelGonzalez.dev

EMAIL: 

Zoom Id:

OFFICE HOURS: Thursdays immediately following class on Thursday evenings via Zoom

COURSE DESCRIPTION: This course covers divisibility theory in the integers, prime numbers, congruences, some number theoretic functions, and Diophantine equations. The material is especially useful for students interested in teaching high school mathematics. 3 sem. hrs. 3 crs. 

PREREQUISITE: Precalculus (Math 201) 

LEARNING OUTCOMES: Upon completion of the course, the student will have: 

1.Developed skills and knowledge on number properties and manipulation,

2.Learned and mastered operations on integers like divisibility and congruence,

3.Developed skills in solving numeral and integer equations,

4.Expanded and applied number theory techniques to real practical situations.

REQUIRED MATERIALS: 

Textbook: Elementary Number Theory (7th Edition) by David M. Burton, McGraw-Hill, 

ISBN 978-0073383149 

 For students considering graduate school: Elementary Methods in Number Theory (Graduate Texts in Mathematics, Vol. 195) (Graduate Texts in Mathematics, 195) 1st Edition by Melvyn Nathanson, Springer, ISBN 978-0387989129

CONTENT: 

Chapter 1 Preliminaries (Mathematical Induction, Binomial Theorem)

Chapter 2 Divisibility 

Chapter 3 Primes and Their Distribution

Chapter 4 Congruences (Modular Arithmetic) 

Chapter 5 Fermat's Little Theorem

Chapter 7 Euler's Generalization of Fermat's Theorem

Chapter 8 Primitive Roots and Indices (optional, time permitting)

Chapter 9 The Quadratic Reciprocity Law

Chapter 10 Introduction to Cryptography

ENABLING ACTIVITIES: Lecture, teamwork, homework, and exams. Homework assignments can be found on my website. 

HOMEWORK: Homework assignments will be assigned weekly after every class. All homework will be collected and graded and feedback will be given during office hours. Exams: All exams will be announced at least 2 weeks in advance. There will be 3 exams for the course in total. 

GRADING POLICY: Your final course grade is computed as follows: Homework: 20% | Exam#1: 22.5% | Exam#2: 22.5% | Final Exam: 35% 

ATTENDANCE POLICY: Good attendance is expected as well as timely arrival to class. Students with excellent participation and attendance will benefit borderline grades. 

FINAL COURSE GRADES: 93-100 A | 90-92.9 A– | 87-89 B+ | 83-86.9 B | 80-82.9 B– | 77-79.9 C+ | 73-76.9 C |70-72.9 C– | 60-69.9 D | 0-59.9 F

BIBLIOGRAPHY: Silverman, Joseph H. A Friendly Introduction to Number Theory. Prentice Hall. Stillwell, John. Elements of Number Theory. Springer. Nathanson, Melvyn. Elementary Methods in Number Theory (Graduate Texts in Mathematics). 

STUDENTS WITH DISABILITIES: 

Mercy College is committed to achieving equal educational opportunities and full participation for persons with disabilities. Persons with disabilities who may need classroom accommodations are encouraged to contact the Office of ACCESSibility before the semester begins to learn about the different accommodations available and the process for obtaining reasonable accommodation(s). Please contact the Office at (914) 674-7523, accessibility@mercy.edu, or visit our website at www.mercy.edu/student-affairs. 

Academic Integrity Policy 

Academic integrity is the pursuit of scholarly activity in an honest, truthful and responsible manner. Students are required to be honest and ethical in carrying out all aspects of their academic work and responsibilities. 

Dishonest acts in a student’s academic pursuits will not be tolerated. Academic dishonesty undermines the College’s educational mission as well as the student’s personal and intellectual growth. In cases where academic dishonesty is uncovered, the College imposes sanctions that range from failure of an assignment to suspension and expulsion from the College, depending on the severity and reoccurrence of the case(s). 

Examples of academic dishonesty include, but are not limited to, cheating, plagiarism, obtaining unfair advantage, and falsification of records and official documents. 

Cheating is the unauthorized use or attempted use of material, information, notes, study aids, devices, or communication during an academic exercise. Examples of cheating include, but are not limited to: 

•Copying from another student during an examination or allowing another to copy your work

•Providing assistance to acts of academic misconduct

•Unauthorized collaboration on a take-home assignment or examination

•Using notes during a closed book examination

•Submitting another’s work as your own

•Unauthorized use during an examination of any electronic device, such as cell phones, computers, or internet access to retrieve or send information

•Allowing others to research or write assigned papers for you or to complete your assigned projects

Plagiarism is the act of presenting another person’s idea, research or writings as your own. Examples of plagiarism include, but are not limited to: 

Copying another person's actual words or images without the use of quotation marks and citations attributing the words to their source 

•Presenting another person's ideas or theories in your own words without acknowledging the source

•Engaging in plagiarism, via the Internet or other web-based or electronic sources, which includes (but is not limited to) downloading term papers or other assignments and then submitting that work as one’s own, or copying or extracting information and then pasting that information into an assignment without citing the source, or without providing proper attribution.

Obtaining unfair advantage is any action taken by a student that gives that student an unfair advantage, or through which the students attempts to gain an unfair advantage in his/her academic work over another student. Examples of obtaining an unfair advantage include, but are not limited to: 

•Gaining advance access to examination materials by stealing or reproducing those materials

•Retaining or using examination materials which clearly indicate the need to return such materials atthe end of the examination

•Intentionally obstructing or interfering with another student’s work

Falsification of Records and Official Documents include, but are not limited to, acts of forging authorized signatures, or falsifying information on an official academic record. 

Consequences for Policy Violation 

A student who is found to be dishonest in submission of his or her academic assignments or other work, or in carrying out his or her academic responsibilities may, at minimum, receive a zero for the submitted assignment, may receive a failing grade for the course, or may be subject to further suspension or expulsion from the College depending on the severity of the offense(s). Regardless, all incidents of academic dishonesty will be reported to the Academic Unit Head and School Dean, and may be retained by the College in the student’s records. 

Reporting 

A faculty member who suspects that a student has committed a violation of the Academic Integrity Policy shall review with the student the facts and circumstances of the suspected violation whenever feasible. Thereafter, a faculty member who concludes that there has been an incident of academic dishonesty sufficient to affect the student's final course grade shall report such incident on the Student Violation of the Academic Integrity Policy Form (located on Mercy Connect under the faculty tab) and submit it to the Dean of the appropriate School. The Dean shall update the Student Violation of the Academic Integrity Policy Form after a suspected incident has been resolved to reflect that resolution. Unless the resolution exonerates the student, the Student Violation of the Academic Integrity Policy Form shall be placed in a confidential academic integrity file created for the purposes of identifying repeat violations, gathering data, and assessing and reviewing policies. 

Academic Sanctions 

If a faculty member believes that the appropriate sanction is academic in nature (e.g., a reduced grade) and the student does not contest either his/her guilt or the particular reduced grade that the faculty member has chosen, then the student shall be given the reduced grade, unless the Dean decides to seek a disciplinary sanction. The reduced grade may apply to the particular assignment where the violation occurred or to the course grade, at the faculty member's discretion. A reduced grade may be an "F", or another grade that is lower than the grade that the student would have earned but for the violation. If a faculty member determines that a student has committed an act of cheating or plagiarism, and the student withdraws from the course, that student will receive an “FW” for the course regardless of the time of withdrawal. The faculty member shall inform the Dean of the resolution via email and the Dean shall update the applicable Student Violation of the Academic Integrity Policy Form to reflect that resolution. 

In a case where a student admits to the alleged academic dishonesty but contests the academic sanction imposed by the faculty member, or in a case where a student denies the academic dishonesty, the student may appeal to the College’s Undergraduate Academic Appeals Committee. 

Judicial Sanctions 

In a case where the allegation of cheating or plagiarism is severe, or where the student has a history of violations of the Academic Integrity Policy which conduct warrants suspension or expulsion from the College, the school Dean shall impose a sanction in addition to or in lieu of academic sanctions, as he/she deems is 

warranted under the circumstances. If the student contests the judicial sanction imposed, he/she may appeal to the Undergraduate Academic Appeals Committee. 

Appeals 

Appeals to the Undergraduate Academic Appeals Committee shall be made within 7 business days of receipt of notice of the academic or judicial sanction. All parties will be permitted to participate and are permitted to submit any documentation they believe is necessary including written statements and documentary evidence. The Undergraduate Academic Appeals Committee shall convene within two weeks of the filing of the appeal submission. The Undergraduate Academic Appeals Committee shall issue a written decision of its finding within 7 business days of convening and shall send copies of its decision to the accused student, the faculty member and the appropriate Dean for archiving in the student’s confidential academic integrity file. 

If the Academic Appeals Committee finds that no violation occurred, the Dean shall remove all material relating to that incident from the student's confidential academic integrity file and destroy the material.