### MATH301: Abstract Algebra I

Unless otherwise noted, homework is due on Tuesday.

Please try to start your homework assignments at least a week in advance. I will give detailed answers to questions during my office hours and hints for questions asked before class. Please feel free to collaborate with other students in the class, but please also be sure that the homework you submit is written in your own words.

The information presented below is a tentative schedule and may change over the course of the semester.

 Date Sections covered and Assignments due 1/24 P: Math Without Fractions P: Proofs by Induction -- Examples of Algebraic Proof 1/29, 1/31 P: Modular Arithmetic P: Equivalence Relations and Partitions 1: Symmetry Groups 2/5, 2/7 Preface: 3, 9, 11, 30 (use Exercise 11?), 50 2: Definition of a Group, Proving things are groups 2/12, 2/14 Chapter 1: 1, 3, 6, 16 due 2/14 2: Proving things about groups 2/19, 2/21 Quiz 1, 2/21 Chapter 2: 1, 2, 3, 11, and use #23 to complete #25; is the group in question Abelian? 3: Order, Finite Groups, 2/26, 2/28 3: Subgroups 3/4, 3/6 Due 3/4; Chapter 3: 7, 11 (hint), 12, 14, 22, 23 3: Center of a Group 3/11, 3/13 Chapter 4: 8(c), 13 (also list elements of and ), 18, 37, 62 4: and Cyclic Groups Quiz 2, 3/13 3/18, 3/20 Spring Break 3/25, 3/27 4: Subgroup Lattices 5: Maps and Permutations 4/1, 4/3 Chapter 4: 32; Chapter 5: 3 (a,c), 6, 13, 21, 23 5: Permutation Groups:  Sn, An 4/8, 4/11 6: Group Isomorphisms 6: Groups acting on themselves: Aut(G) and Cayley's Theorem 4/15, 4/17 Quiz 3, 4/15 Chapter 6:  1, 3, 10 due 4/17 Rings 4/22, 4/24 Integral Domains Fields 4/29, 5/1 Quiz Redo and all late homework due 4/29 Fields Chapter 12:  2, 3, 6; Chapter 13:  3, 5, 26 due 5/1 Review for Final Sample Final 5/13 Final Exam, 2:00-4:00PM The final exam will take the form of a short homework assignment on rings, integral domains and fields.  It will be open book/open note.

MATH318