Instructor: | Arvind Ayyer |
Office: | X-15 (new wing) |
Office hours: | Tuesday, 4-5pm |
Phone number: | (2293) 3215 |
Email: | (First name) at iisc dot ac dot in |
Class Timings: | Mondays, Wednesdays and Fridays, 11:00 — 11:50am |
Classroom: |
G - 21, OPB To join the course on MS Teams, use the code gmw03ii |
Textbooks: |
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TAs and office hours: |
Email ids are in paranthesis and end with at iisc dot ac dot in, and offices are in the maths department.
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Tutorials: | Tuesdays 9:00 — 9:50am, G-01 and G-21 |
The date for the midterms and final will be announced later.
Here are the weights for the homework and exams.
All marks will be posted online on Teams.
week | date | sections | material covered | homework and other notes |
1 | 1/1 | Class cancelled |
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2/1 | - | Class cancelled |
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3/1 | (T) 2.1-2.3 | Peano axioms | No homework :) | |
5/1 | Class cancelled |
- | ||
2 | 8/1 | (T) 3.1 | Basic axioms | 2.2.1, 2.2.4, 2.2.6, 2.3.2, 2.3.4 3.1.1, 3.1.3, 3.1.7, 3.1.10 |
9/1 | - | Discussion |
- | |
10/1 | (T) 3.3, 3.4 | Relations and functions | 3.4.1, 3.4.3, 3.4.4 | |
12/1 | (T) 3.3, 3.6, 8.1, 8.3 |
Cardinalities of sets, countability | 3.3.2, 3.3.5, 3.6.7, 3.6.6 8.1.2, 8.1.6, 8.3.3 |
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3 | 15/1 | (T) 8.4, 8.5 | Axiom of choice, Zorn's lemma | 8.4.1, 8.5.3, 8.5.11, 8.5.18 |
16/1 | - | Quiz 1 |
- | |
17/1 | (T) 4.1 - 4.4 | Integers, rationals and gaps in them | 4.1.3, 4.1.8, 4.2.6, 4.4.2(a) | |
19/1 | (B) 1.1-1.2 2.1-2.2 |
Pigeonhole principles and mathematical induction | Chap. 1: 2, 4, 9, 13 Chap. 2: 3, 5, 8, 11 |
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4 | 22/1 | (B) 3.1-3.3 | Permutations, choices and the binomial theorem | Chap. 2: 14, 28 Chap. 3: 1, 3, 7, 15, 21 |
23/1 | - | Discussion |
- | |
24/1 | (B) 4.3, 5.1, 5.3 | Combinatorial identities, compositions and partitions | Chap. 4: 3, 5, 9, 18 Chap. 5: 1, 7, 11 |
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26/1 | Holiday |
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5 | 29/1 | (B) 5.2, 6.1 | Set partitions | Chap. 5: 2, 4(a), 5, 16 |
30/1 | - | Quiz 2 |
- | |
31/1 | (B) 7.1-7.2 | Permutations by cycles | Chap. 6: 2, 5, 8, 14, 17, 18, 22 | |
2/2 | (B) 8.1 | Inclusion-Exclusion formulas and Ordinary generating functions |
Chap. 7: 1, 9, 13 Chap. 8: 1, 2, 8, 9 |
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6 | 5/2 | (B) 8.2 | Exponential generating functions | Chap. 8: 3, 16, 19, 20 |
6/2 | - | Discussion |
- | |
7/2 | (B) 9.1 | Graph theory definitions and Eulerian tours | Chap. 9: 2, 8, 12, 16 | |
9/2 | (B) 10.1 | Trees and Cayley's formula | Chap. 10: 2, 5, 7, 10, 15 | |
7 | 12/2 | (B) 10.4 | Spanning trees and the matrix-tree theorem | Chap. 10: Example 10.22, 16, 18(b, c), 20 |
13/2 | - | Quiz 3 |
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14/2 | (B) 12.1 | Planar graphs | Chap. 11: Example 12.4, Cor. 12.7, Prop. 12.8 | |
16/2 | - | Exam week |
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8 | 19/2 | Midsemester exam |
- | |
20/2 | - | Exam week |
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21/2 | Exam week |
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23/2 | Exam week |
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9 | 26/2 | (IR) 1.1 | Unique factorization in integers | Chap. 1: 1, 6, 10, 11 |
27/2 | - | Discussion |
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28/2 | (IR) 1.1-1.2 | Unique factorization in polynomial rings | Chap. 1: 7, 13, 19, 20 | |
1/3 | (IR) 1.3-1.4 | Principal ideal domains, Z[i] and Z[ω] | Chap. 1: 31, 34, 36, 37 | |
10 | 4/3 | (IR) 2.1 | Infinitude of primes and Dirichlet's theorem | Chap. 1: 33, 35 Chap. 2: 1, 4, 6, 16, 17 |
5/3 | - | Quiz 4 |
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6/3 | (IR) 2.2 | Arithmetic functions | Chap. 2: 9, 10, 11, 13, 15, 22 | |
8/3 | Holiday |
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11 | 11/3 | (IR) 3.1-3.3 | Congruences in Z | Chap. 3: 2, 3, 4, 8 |
12/3 | - | Discussion |
- | |
13/3 | (IR) 3.3-3.4 | Euler's theorem, Fermat's little theorem and Chinese Remainder Theorem | Chap. 3: 5, 12, 16, 23 | |
15/3 | (IR) 4.1 | Units in Zn | Chap. 4: 2, 4, 5, 13, 14, 22 | |
12 | 18/3 | (IR) 5.1 | Quadratic residues | Chap. 5: 2, 3, 6, 14, 15 |
19/3 | - | Quiz 5 |
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20/3 | (IR) 5.2-5.3 | Law of quadratic reciprocity | Chap. 5: 1, 6, 7, 10, 12, 16(i) | |
22/3 | (DF) 1.1-1.2 | Basic properties of groups | Sec. 1.1: 1, 5, 9, 12, 13, 20 Sec. 1.2: 4, 9, 10 |
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13 | 25/3 | (DF) 1.3-1.6 | Examples of groups, homomorphisms and isomorphisms | Sec. 1.2: 7, 18 Sec. 1.3: 4, 10, 11, 15 Sec. 1.6: 1, 2, 5, 11, 18 |
26/3 | - | Discussion |
- | |
27/3 | (DF) 1.7, 2.1 | Group actions Subgroups |
Sec. 1.7: 2, 6, 8, 11, 15 Sec. 2.1: 1, 3, 5, 9 |
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29/3 | Holiday |
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14 | 1/4 | (DF) 2.2-2.3 | Centralizers, normalizers and cyclic groups | Sec. 2.2: 2, 3, 5(a), 6(a), 10 Sec. 2.3: 2, 12, 16 |
2/4 | - | Quiz 6 |
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3/4 | (DF) 2.3, 31 | Subgroups of cyclic groups and quotient groups | Sec 2.3: 20, 24 Sec 3.1: 1, 2, 6, 9, 11 |
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5/4 | (DF) 3.1 | Quotient groups and cosets | Sec 3.1: 12, 14(a, b), 22(a), 24, 26(a, b), 36 | |
15 | 8/4 | (DF) 3.2, 3.3 | Lagrange's theorem and first isomorphism theorem | Sec 3.2: 4, 5, 6, 10, 15 |
9/4 | - | Discussion |
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10/4 | (DF) 4.1-4.3 | Cayley's theorem and class equation | Sec 4.1: 1, 4, 9(a) Sec 4.2: 1, 2, 9, 11 Sec 4.3: 2, 4, 10 |
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19 | 22/4 | - | Final Exam |