Outline of Course Content: The aim of this course is to introduce foundational topics in mathematics to facilitate research in general computer science and mathematics (and not just theoretical computer science).

Evaluation of students will be based on five homework (45%), a late mid-term exam in the 10-th week (30%), a final presentation (20%), and class participation (5%). Students will be encouraged to collaborate and discuss among themselves for homework.

Prerequisites: Mastery of the material covered in Calc III (Math 261), Linear Algebra (Math 265), Probability (STAT 416), Foundations of CS (CS 182), and Analysis of Algorithms (CS 381 or CS 580).

Course Requirements: Students should attend most of the classes and read the text. Some material on the exams will appear only in the text or only in class. There will be one midterm exam and one final exam. There will be five homework. The grading weights will be 45% homework, 20% midterm exam, 30% final exam, and 5% class participation. Solving extra credit problems in homework earns you the goodwill of the instructor, which can result in an increment of the final grade in borderline cases. Homework submissions must be formatted using Latex.

Course Materials: There is no official textbook for this course. Each lecture will be accompanied by lecture slides, pointers to additional reading materials, surveys, and videos. Additional links will be provided to supplementary reading materials and other courses which are similar in spirit to this course.

Most of the following material is based on the policy followed by Prof. Samuel Wagstaff in his cryptography courses.

Course Policy: Students may ask the instructor questions by email. These email questions will be answered as soon as possible. Students may leave and enter the class room during class, but should try to do so quietly. Cell phones should be turned off during class. Students who need to use a phone, either to talk or text, during class should leave the room. Students may use (laptop) computers during class.

Grading: All re-grading of homework and midterm exam must be done within two weeks of the day the work was returned to the class.

Academic Dishonesty: Purdue prohibits "dishonesty in connection with any University activity. Cheating, plagiarism, or knowingly furnishing false information to the University are examples of dishonesty." Furthermore, the University Senate has stipulated that "the commitment of acts of cheating, lying, and deceit in any of their diverse forms (such as the use of substitutes for taking examinations, the use of illegal cribs, plagiarism, and copying during exams) is dishonest and must not be tolerated. Moreover, knowingly to aid and abet, directly or indirectly, other parties in committing dishonest acts is in itself dishonest." While it is all right to discuss homework in this class with other students in general terms, do not copy another student's homework or let anyone copy your homework. These discussions should be appropriately acknowledged. When two identical homeworks are found, both are sent to the Dean of Students to determine who copied from whom.
Students may use calculators during exams. They may not use cell phones, computers, notes, cheat sheets, photographic equipment, radios, televisions, books, Morse code, signals or sign language during exams. Do not look at exams of other students or let others see your exam while the exam is in progress. Communicate only with the instructor during an exam.
Penalties for academic dishonesty range from a 0 grade on one assignment to a failing grade in the class and even expulsion from the University. A hearing at the Dean of Students' Office can ruin your whole day.

Attendance: University policy states that students are expected to attend every meeting of every class in which they are enrolled. Only the instructor can excuse a student from a course requirement or responsibility. When conflicts or absences can be anticipated, such as for job interviews and religious observances, the student should inform the instructor in advance of the situation and plan to make up the missed work. For unanticipated or emergency absences when advance notification to an instructor is not possible, the student should contact the instructor by email. When direct contact with the instructor is not possible because of circumstances beyond the student's control, or in cases of bereavement, the student or the student's representative should contact the Office of the Dean of Students.
Federal law requires instructors to take attendance at least once near the beginning of the semester and again near the end of the semester. (The purpose of this law is to insure that students who receive financial aid actually take and attend classes.) Other than these two occasions, I will not take attendance in class. You should attend class because (1) either you paid for it or someone else paid for you to attend and (2) I might discuss a topic in class that is not in the text, but will appear on an exam. Make friends with other students in class so that you can copy their notes when you miss a class.

Grief Absence Policy: Purdue University recognizes that a time of bereavement is very difficult for a student. The University therefore provides the following rights to students facing the loss of a family member through the Grief Absence Policy for Students (GAPS). GAPS policy: Student will be excused for funeral leave and given the opportunity to earn equivalent credit and to demonstrate evidence of meeting the learning outcomes for missed assignments or assessments in the event of the death of a member of the student's family.

Missed or Late Class Work: If a student misses a homework because he or she didn't get around to doing it, then the grade will be 0 for that homework. If a student has a planned absence for a class when homework is due, the student should turn in the homework before it is due or email it to the instructor by the time it is due. There is a penalty for late homework in this case. Homework will be accepted late without penalty in case of serious illness or bereavement.
If a student misses an exam, then the grade will be 0 for that exam, except in case of serious illness or bereavement, in which case the student will be given an opportunity to make up the exam. If a student has a planned absence for a class when an exam will be given, the student should make arrangement before the planned absence to take the exam early or to take a makeup exam after returning to campus.

Violent Behavior Policy: Purdue University is committed to providing a safe and secure campus environment for members of the university community. Purdue strives to create an educational environment for students and a work environment for employees that promote educational and career goals. Violent behavior impedes such goals. Therefore, violent behavior is prohibited in or on any University facility or while participating in any university activity.

Students with Disabilities: Purdue University is required to respond to the needs of the students with disabilities as outlined in both the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990 through the provision of auxiliary aids and services that allow a student with a disability to fully access and participate in the programs, services, and activities at Purdue University.
The ODOS Testing Center is an excellent place for students with disabilities to take exams for this class. Please tell the instructor at least one week in advance if you wish to take the exams there. If you have a disability that requires other special accommodation, please tell the instructor early in the semester. It is the student's responsibility to notify the Disability Resource Center of an impairment/condition that may require accommodations and/or classroom modifications.

Emergencies: In the event of a major campus emergency (such as a tornado, earthquake, flu epidemic or terrorist attack), course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructor's control. Relevant changes to this course will be posted onto the course website or can be obtained by contacting the instructor via email or phone. You should read your Purdue email frequently.

Nondiscrimination: Purdue University is committed to maintaining a community which recognizes and values the inherent worth and dignity of every person; fosters tolerance, sensitivity, understanding, and mutual respect among its members; and encourages each individual to strive to reach his or her own potential. In pursuit of its goal of academic excellence, the University seeks to develop and nurture diversity. The University believes that diversity among its many members strengthens the institution, stimulates creativity, promotes the exchange of ideas, and enriches campus life.
Purdue University prohibits discrimination against any member of the University community on the basis of race, religion, color, sex, age, national origin or ancestry, marital status, parental status, sexual orientation, disability or status as a veteran. The University will conduct its programs, services and activities consistent with applicable federal, state and local laws, regulations and orders and in conformance with the procedures and limitations as set forth in Executive Memorandum No. D-1, which provides specific contractual rights and remedies.
The instructor agrees completely with all Purdue policies mentioned in this document.

Privacy: The Federal Educational Records Privacy Act (FERPA) protects information about students, such as grades. If you apply for a job and wish to use the instructor as a reference, you should tell the instructor beforehand. Otherwise, the instructor cannot say anything about you to a prospective employer who might call. The instructor is happy to provide references and to write letters of recommendation for his students as needed.

The syllabus is subject to change.