# Applied Math 106: Applied Algebra ## Lecture Notes, Handouts, and Assignments To compile LaTeX versions of lecture notes, use [macros.tex](https://people.seas.harvard.edu/~salil/am106/fall18/macros.tex) and [header.tex](https://people.seas.harvard.edu/~salil/am106/fall18/header.tex). Sort**Date****Title****Notes****Reading**Tue 9/4 Course Overview, Induction [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/IntroInduction.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/IntroInduction.tex) Gallian Ch. 0 Thu 9/6 The Integers [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Integers.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Integers.tex) Gallian Ch. 0 Problem Set 0 (due 9/14) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps0.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps0.tex) Tue 9/11 Modular Arithmetic, Relations, Algorithms [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ModRelationsAlgorithms.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ModRelationsAlgorithms.tex) Thu 9/13 Measuring Complexity, The Euclidean Algorithm [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Euclidean.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Euclidean.tex) Problem Set 1 (due 9/21) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps1.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps1.tex) Tue 9/18 Extended Euclid, Primality & Factoring, Intro to Groups [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Groups.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Groups.tex) Gallian Ch. 2 Thu 9/20 More Groups and Basic Properties [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/MoreGroups.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/MoreGroups.tex) Gallian Ch. 1,2 Problem Set 2 (due 9/28) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps2.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps2.tex) Tue 9/25 Subgroups, Cyclic Groups [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/SubgroupsCyclic.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/SubgroupsCyclic.tex) Gallian Ch. 3,4 Thu 9/27 Cyclic Groups & Cryptography [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/CyclicCrypto.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/CyclicCrypto.tex) Gallian Ch. 4 Practice Quiz I Tue 10/2 Permutation Groups [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/PermutationGroups.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/PermutationGroups.tex) Gallian Ch. 5 Thu 10/4 Quiz I Problem Set 3 (due 10/12) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps3.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps3.tex) Tue 10/9 Isomorphisms and Cosets [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/IsomorphismsCosets.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/IsomorphismsCosets.tex) Gallian Ch. 6-7 Thu 10/11 Cosets [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Cosets.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Cosets.tex) Gallian Ch. 7 Problem Set 4 (due 10/19) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps4.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps4.tex) Tue 10/16 Direct Products [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/DirectProducts.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/DirectProducts.tex) Gallian Ch. 8, 11 Thu 10/18 Normal Subgroups & Factor Groups [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/NormalandFactor.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/FactorandHomomorphisms.tex) Gallian Ch. 9 Problem Set 5 (due 10/26) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps5.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps5.tex) Tue 10/23 Homomorphisms, Isometries [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/HomomorphismsandIsometries.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/HomomorphismsandIsometries.tex) Gallian Chs. 10, 27 Thu 10/25 Group Theory & Crystallography [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Crystallography.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Crystallography.tex), [handout](https://people.seas.harvard.edu/~salil/am106/fall18/CrystallographyHandout.pdf) Gallian Ch. 28 Problem Set 6 (due 11/2) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps6plus.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps6.tex) Tue 10/30 Rings [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Rings.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Rings.tex) Gallian Chs. 12, 13 Thu 11/1 Properties of Rings [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/RingProperties.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/RingProperties.tex) Problem Set 7 (due 11/10) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps7.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps7.tex) Tue 11/6 EthiCS Module led by [Kate Vredenburgh](https://philosophy.fas.harvard.edu/people/kate-vredenburgh): Basic vs. Applied Research [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/EthiCS.pdf) [Effective Altruism](https://www.effectivealtruism.org/articles/introduction-to-effective-altruism/), [Strangers Drowning](https://people.seas.harvard.edu/~salil/am106/fall18/Excerpt%20from%20Strangers%20Drowning.pdf), [Mathematician's Apology](https://people.seas.harvard.edu/~salil/am106/fall18/A%20Mathematician's%20Apology%20-%20selections.pdf) Thu 11/8 Ideals and Factor Rings [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Ideals.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Ideals.tex) Gallian Ch. 14 Practice Quiz II [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/quiz2-practice.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/quiz2-practice.tex) Tue 11/13 Ring Homomorphisms [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Homomorphisms.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Homomorphisms.tex) Gallian Ch. 15 Thu 11/15 Quiz II Problem Set 8 (due 11/30) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps8.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps8.tex) Tue 11/20 Polynomial Rings [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/PolyRings.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/PolyRings.tex) Gallian Ch. 16 Thu 11/22 No Class - Thanksgiving Tue 11/27 Factorization & Ideals in Polynomial Rings, Field Extensions [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/PolyFactorizationAndIdeals.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/PolyFactorizationAndIdeals.tex) Gallian Chs. 16-17 Thu 11/29 Vector Spaces [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/VectorSpaces.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/VectorSpaces.tex) Gallian Ch. 19 Problem Set 9 (due **Monday** 12/10) [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/ps9.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/ps9.tex) Tue 12/4 Error-Correcting Codes [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Codes.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Codes.tex) Thu 12/6 Conclusions [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/Conclusions.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/Conclusions.tex) Final Exam Practice [pdf](https://people.seas.harvard.edu/~salil/am106/fall18/final-practice.pdf), [tex](https://people.seas.harvard.edu/~salil/am106/fall18/final-practice.tex) Thu 12/13 Review Session I (7-9pm, MD 223) Sun 12/16 Review Session II (7-9pm, MD 223) Wed 12/19 Final Exam (9am-12pm, Harvard Hall 102)