My email address is freudro8@gmail.com.
Course syllabus : AL1 Introduction to abstract algebra
General information
Final is on July 31; Info and sample final
We shall discuss the sample final problems in the July 30 class.
Midterm is on July 3; Info and sample midterm
We shall discuss the sample midterm problems in the July 2 class.
New deadline to submit HW3--6 (in pdf by email): Friday 23:59.
As agreed, there are no classes on Thursdays after July 8.
June 10: Problem sheet 1: Divisibility and congruences , Handout 1: Basic number theory , Summary
June 11: Problem sheet 2: Binomial theorem , Handout 2: Binomial theorem , Summary
June 12 Problem sheet 2: Complex numbers , Handout 2: Complex numbers , Summary
June 13 Problem sheet 3: Operation, rings, and fields , Handout 3: Operation, rings, and fields , Summary
Week 1: Homework 1 , due on June 19, Summary June 10-13
June 17 Problem sheet 4: Subring , Handout 4: Subring , Summary
June 18 Problem sheet 4: Ideal , Handout 4: Ideal , Summary
June 19 Problem sheet 5: Factor ring , Handout 4: Factor ring , Summary
June 20 Summary
Week 2: Homework 2 , due on June 26, Summary June 17-20
June 24 Problem sheet 5: Homomorphism , Handout 4: Homomorpism , Summary
June 25 Problem sheet 6: Direct sum , Handout 5: Direct sum , Summary
June 26 Problem sheet 6: Number theory in rings , Handout 5: Number theory in rings , Handout 6: UFT, PID, ED , Summary
June 27 Problem sheet 7: Gaussian integers , Summary
Week 3: Homework 3 , due on July 4(!), Summary June 24-27
July 1 Problem sheet 7: Gaussian integers and sums of two squares , Handout 7: Gaussian integers and Two Squares Theorem , Summary
July 2 Review session: Sample midterm
July 3 Midterm
July 4 Problem sheet 8: Finite fields , Handout 8: Finite fields and Sidon sets , Summary
Week 4: Homework 4 , due on July 12, 23:59 Summary July 1-4
July 8 Problem sheet 8: Sidon sets , Handout 8: Sidon sets , Summary
July 9 Problem sheet 9: Groups , Handout 9: Groups , Summary
July 10 Problem sheet 9: Cyclic groups, subgroups , Handout 9: Cyclic groups, subgroups , Summary
Week 5: Homework 5 , due on July 19, 23:59 Summary July 8-10
July 15 Problem sheet 10: Normal subgroups , Handout 10: Normal subgroups , Summary
July 16 Problem sheet 10: Factor group, group homomorphism , Handout 10: Factor group, group homomorphism , Summary
July 17 Problem sheet 10: Direct product , Handout 10: Direct product , Problem sheet 11: Structure of groups , Handout 11: Structure of groups , Summary
Week 6: Homework 6 , due on July 26, 23:59 Summary July 15-17
July 22 Final info and sample final , Exercise 116: The real function f(x)=x is the sum of two periodic functions , Summary
July 23 Problem sheet 11: Permutation groups , Handout 12: Group theory in Social sciences , Summary
July 24 Problem sheet 11: Permutation groups , Handout 13: Burnside's lemma , Summary
July 29 Problem sheet 11: Decomposition into a direct product, the converse of Lagrange's theorem , Handout 14: The converse of Lagrange's theorem , Summary
July 30 Review session: Sample final
July 31 Final
Weeks 7-8: Summary July 22-31