UM 203. Introduction to Algebraic Structures - Spring 2019 - Vamsi Pingali


Unfortunately, no single book will do. The texts we will be following are as follows. The first two will be our main textbooks.



Instructor : Vamsi Pritham Pingali, vamsipingali@iisc.ac.in

Office : N23 in the mathematics building. (It might be a good idea to email me if you plan on coming to my office.)

Teaching assistants : K. Hariram (hariramk@iisc.ac.in) and Abhash Kumar Jha (abhashjha@iisc.ac.in).

Classroom and timings : Tuesdays and Thursdays 5:30-6:30 PM and Wednesdays 12-1 in Room G2 (Old physics building).

The Grading policy : 15% for Tests based on HW, Midterm-35%, and 50% for the Final. Under NO circumstances will makeup exams be held for the midterms. If you have a valid and provable excuse, (Schedule conflicts with other courses do NOT constitute as valid excuses. You are supposed to resolve them before registering for the courses.) then your performance on the other exams shall determine your grade on your midterms.


Exams : The dates for the midterm and the final will be announced later on.

Ethics: Read the information on the IISc student ethics page. In short, cheating is a silly thing. Don't do it. As for homeworks, write them up on your own. You are allowed to discuss them amongst yourselves but please write the solutions on your own. That said I must hasten to add that you learn mathematics best when you solve the problems entirely by yourself.

Here is the tentative schedule. (It is subject to changes and hence visiting this webpage regularly is one of the best ideas in the history of best ideas.)

Wk

 Dates

 Syllabus to be covered

1

1 Jan - 7 Jan

Logistics, Naive set theory done right (Tuesday notes); Axiom of Choice, Equivalence relations, Involutions (Wednesday notes); Partial orders and Zorn's lemma, Cardinality (Thursday notes)

2

8 Jan - 14 Jan

Integers and Rationals (Tuesday notes), Complete induction and the pigeon-hole principle(Wednesday notes), Permutations and Combinations (Thursday notes)

3

15 Jan - 21 Jan

Cycles in permutations (Tuesday notes), Ordinary generating functions (Wednesday notes), Combinatorics and O.G.Fs (Thursday notes)

4

22 Jan - 28 Jan

5

29 Jan - 4 Feb

6

5 Feb - 11 Feb

7

12 Feb - 18 Feb

8

19 Feb - 25 Feb

9

26 Feb - 4 March

10

5 March - 11 March

11

12 March - 18 March

12

19 March - 25 March

13

26 March - 1 April

14

2 April - 8 April



The final exam week is TBA.

HW - Kyon ki teacher bhi kabhi student tha....

Wk

 Test to be held on

 Homework (subject to changes; please check regularly)

2

11 Jan

HW 1

4

25 Jan

HW 2