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MATH 23B: INTRODUCTION TO PROOFS, SECTION 2, FALL 2022

Overview. The main goal of this course is to become comfortable reading and writing mathematical texts; we will speciﬁcally focus on proofs. Another purpose of this course is to develop your ability to think like a mathematician (not only about mathematics). You will see that mathematics has a lot of very diﬀerent sides and it is not only computations. We will introduce basic mathematical notions and some aspects of mathematical logic. Diﬀerent techniques of proofs will be presented. The only way to learn these techniques is to practice, you will try to ﬁnd your own solutions.

Classes will consist of both lectures and discussions. Because of this, repeated absences will result your grade reduction.

Homework. Weekly sets of homework will be assigned. They will mainly include writing down proofs of mathematical statements. Please write down your proofs as detailed as possible. Part of homeworks should be handwritten on paper and scanned (camera scanning is ﬁne). The other part must be written in LATEX.

We will grade each homework twice. At ﬁrst you will receive only points without any comments. It is your challenge to ﬁnd mistakes and ﬁx them.

Discussions with other students are allowed, however, we strongly recommend to spend time thinking about the homework problems on your own before any discussion. You are required to write solutions in your own words without help from anyone.

Team review of a scientiﬁc talk. Students will be divided into groups. Each group will need to attend a scientiﬁc talk (video is ﬁne), discuss it and prepare a review of the talk.

Midterm and ﬁnal. Midterm consists of several problems, which are mostly easier than problems in weekly homeworks. Your challenge will be to write correct proofs in a limited time.

Final exam will be ”take home” and problems will be similar to homeworks. However you will not be able to discuss them with other students.

Grading.

• Homework: 40%

• Class participation: 10%

• Team review: 10%

• Midterm: 20%

• Final: 20%

Credit hours. Success in this 4 credit hour course is based on the expectation that students will spend a minimum of 9 hours of study time per week in preparation for class (readings, homework, preparation for exams, etc.).

Disability support. “Brandeis seeks to welcome and include all students. If you are a student who needs accommodations as outlined in an accommodations letter, please talk with me and present your letter of accommodation as soon as you can. I want to support you. In order to provide test accommodations, I need the letter more than 48 hours in advance. I want to provide your accommodations, but cannot do so retroactively. If you have questions about documenting a disability or requesting accommodations, please contact Student Accessibility Support at 781-736-3470 or [email protected].”

Academic integrity. “You are expected to be honest in all of your academic work. Please consult Brandeis University Rights and Responsibilities for all policies and procedures related to academic integrity. Students may be required to submit work to TurnItIn.com software to verify originality. Allegations of alleged academic dishonesty will be forwarded to the director of academic integrity. Sanctions for academic dishonesty can include failing grades and/or suspension from the university. Citation and research assistance can be found on the university library website.”