MAT165

Gateway to Abstract Reasoning

Information

Instructor: Dr Manjil P. Saikia

Contact: [email protected] (please only use this email address to send me emails related to this course)

Lecture Time & Place: Wednesdays & Fridays 1100 to 1215 (Room XXX, SAS)

Office Hours: By appointment (Room 325, SAS)

Attendance Policy: Attendance is mandatory, check the institute’s attendance policy on AURIS (please note, we have a new policy from last semester). If you are low on attendance then you should talk to me (at least 3 weeks before the end-semester examination).

Course Details

Available on AURIS, we will follow the syllabus (more or less), but there will be a few digressions. So, I encourage you to keep notes.

Reading Materials

There is no fixed textbook for this course. I will try to provide the materials to be discussed before each lecture. Students are expected to read up on the shared material. In addition, I will share resources below after every lecture.

To get a high-level overview of mathematics, I recommend Mathematics: A Very Short Introduction by Timothy Gowers (Oxford University Press, 2002).

Grading

  • Assignment: There will be a weekly assignment based on the materials covered in the respective week. This will contribute 20% to the total score.
  • Presentation: Students are expected to learn a mathematically rigorous proof of their favourite result and present it. This will contribute 20% to the total score.
  • Written Report: Students will have to write the content of their presentation in an article format, and submit at least 2 days before their presentation. This will contribute 20% to the total score.
  • Mid-Semester Examination: We will have a 120-minute written exam (closed book), this will count towards 20% of the total score.
  • End-Semester Examination: We will have a 120-minute written exam (closed book), this will count towards 20% of the total score.

To get an A grade, you must score atleast 80% overall. However, this doesn’t automatically guarantee an A.

Lectures

W 08/10: Introduction to the course, historical overview of mathematical thought
F 10/11: How mathematics helped shape civilization? & The Evolution of Trust
W 15/10: Basic proof ideas, identities, proof without words, Pythagoras’ theorem
F 17/10: More proof ideas, irrationality of $\sqrt{2}$ and $\phi$
F 24/10: Principle of Mathematical Induction (PMI)
W 29/10: Problems on PMI
F 31/10: Problems on PMI & Problems on parity
W 05/11: Introduction to combinatorics
F 07/11: Bijections and double counting
W 12/11: Problems on combinatorics
F 14/11: Problems on combinatorics
M 17/11: Division Algorithm and GCD
W 19/11: Congruences and Divisibility tests
W 26/11: Problems on elementary number theory
T 02/12: Mid-Semester Examination
W 07/01: Pigeonhole Principle (PHP) and Applications
F 09/01: Problems on PHP
F 16/01: More problems (PHP and others)
W 21/01: Invariants and Colourings
F 23/01: Guest Lecture by Professor Aalok Thakkar
W 28/01: Invariants and Colourings
F 30/01: Problems on Invariants and Colourings
S 31/01: Basic introduction to Graphs
S 31/01: Problems on Graphs
S 31/01: Guest Lecture by Professor Pravakar Paul
W 04/02: Countable & Uncountable Sets
F 06/02: Topology and its applications

Assignments

  • The problem sets will be updated over the semester. I will announce this in class when I post a set here.
  • To get the most out of this course, you are expected to spend at least twice the amount of lecture hours on your own.

Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5
Assignment 6

Submissions

  • Due time: as mentioned on the sheet
  • Must be submitted as PDF (via email) or printed/written (slide under my office door)
  • Begin each solution on a new page, and use only blank or dotted pages (not ruled)
  • Staple the submission, if submitting a paper version
  • State your sources at the top of each problem (even if you worked independently)

Late Policy

  • Penalty: Late submissions will be penalized by 25% per each late day
  • Extensions: There will be no extensions given

Collaborations

  • You are encouraged to first work on the problems independently before seeking collaboration.
  • Meaningful collaboration is allowed and is encouraged for this course.
  • You must write up your solutions.

Acknowledging collaborators and sources

It is required to acknowledge your sources (even if you worked independently).

  • At the beginning of the submission for each problem, write Collaborators and sources: followed by a list of collaborators and sources consulted (people, books, papers, websites, software, etc.), or write none if you did not use any such resources.
  • Failure to acknowledge will result in an automatic 20% penalty per problem.
  • Acceptable uses of resources include: looking up a standard theorem/formula/technique; using Wolfram Alpha/Mathematica/Python for a calculation (no need to mention lectures)
  • Unacceptable uses of resources include: directly looking up the problem online or in the research literature for a solution. (Once you have solved a problem, it is fine to seek and learn alternate solutions.)

Intentional violations of the above policies may be considered academic dishonesty/misconduct.

(Thanks to Professor Yufei Zhao for his extensive course policy page, from which I have created my policies.)