Introduction to Mathematical Proof

MTH 301, Fall 2023

Mondays and Wednesdays, 12:20 - 2:15 pm, 1S-102


Course Information Help Course schedule Blackboard Policies FAQs Department of Mathematics

Instructor: Professor Abhijit Champanerkar

Office: 1S-230
Email :
Office Hours: Mon-Wed 2:15 - 3:15, or by appointment.
Class Homepage: http://www.math.csi.cuny.edu/abhijit/301/ (this page)
Academic Calendar


Course Information

Course description: The goals of this course are for you to become adept at logical reasoning by learning mathematical processes that are essential for studying higher mathematics. We will focus especially on the idea of a mathematical proof. We will learn how to (1) understand mathematics in its three modes of communication - hearing, reading and writing, and (2) discover mathematics by exploration and experimentation. You will have succeeded in this course if by the end of the semester you understand or have learned
Text Book and Syllabus: Fendel and Resek, Foundations of Higher Mathematics , Pearson ISBN 9780201125870. We will cover Chapters 1 to 6 from the text book. See below for a tentative list of topics by dates for this semester.

The first 6 chapters of the textbook will be supplied to students on the first day of classes. Please note that you may not distribute, photocopy any parts of this material at any time, and students have to return the textbook at the end of the semester. Please bring the textbook to every class.

Attendance and class participation: Both will count towards the final grade.

Homework, Quizzes and Exams Practising the concepts learned in the class and their assessment will be in the following ways:


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Course schedule and Homework Here is a tentative list of topics by week for this semester. Note that this schedule may change depending on how the class progresses.



Week Date Topic Homework & Quizzes
1 Aug 28 1.1 Exploration
1.2 From Exploration to Proof
2* Sept 4 1.3 Proof: An Introduction HW 1 Due: Mon Sept 11
3 Sept 11 1.3 Proof: An Introduction HW 2 Due: Wed Sept 20
4 Sept 18 2.1 Exploring Sets HW 3 Due: Mon Oct 3rd
5* Sept 25 2.2 Proofs about Sets, 2.3 Exploring Integers
6 Oct 2 2.4 Proofs about Integers HW 4 Due: Mon Oct 16
7 Oct 9 Review and Exam 1 Sample Problems for Exam 1
8 Oct 16 3.1 Quantifiers HW 5 Due: Wed Oct 25
9 Oct 23 3.1 Quantifiers
10 Oct 30 3.2 Working with Quantifiers HW 6 Due: Wed Nov 8th
11 Nov 6 4.1 Proofs with Quantifiers HW 7 Due: Mon Nov 20th
12 Nov 13 4.2 Equivalences in Proofs
13* Nov 20 5.1 Induction part 1
14 Nov 27 Review and Exam 2 Sample Problems for Exam 2
15 Dec 4 5.1 Induction HW 8 Due: Mon Dec 11th
16* Dec 11 Review for Final Exam
Final Exam: Wednesday Dec 20th, class time Sample Problems for Final


Note:



Course Policies

Course policy: Without exception you must pass all the exams to pass this course. You must take the final exams at the time scheduled by the university. Any changes to the grading policy will be announced in the class.

Textbook Return Policy: Failure to return the textbook on day of the final exam will result in a F grade in the course.

Academic dishonesty: Cheating will not be tolerated. Please see CUNY Policy on Academic Integrity.

Disability policy: Qualified students with disabilities will be provided reasonable academic accommodations if determined eligible by the Center for Student Accessibility. Prior to granting disability accommodations in this course, the instructor must receive written verification of student’s eligibility from the Center for Student Accessibility, which is located in 1P-101. It is the student’s responsibility to initiate contact with the Center for Student Accessibility staff and to follow the established procedures for having the accommodation notice sent to the instructor.