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Abstract Algebra

by: Alvena McDermott

Abstract Algebra MATH 3330

Alvena McDermott
GPA 3.69


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This 2 page Class Notes was uploaded by Alvena McDermott on Saturday September 19, 2015. The Class Notes belongs to MATH 3330 at University of Houston taught by Staff in Fall. Since its upload, it has received 36 views. For similar materials see /class/208414/math-3330-university-of-houston in Mathmatics at University of Houston.


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Date Created: 09/19/15
Math 3330 Summer 2009 MidTerm Review Notes De nitions you should know Maps 7 what is an injective surjective or bij ective map Binary Operations 7 What does it mean for a binary operation to be associative commutative have an identity be closed or for an element to have an inverse Relations What is a re exive relatrion What is a symmetric relation What is a transitive relation What is an equivalence relation Integers 7 what are the properties of the greatest common divisor between two numbers What does relatively prime mean De ne a group De ne a subgroup De ne the cyclic group generated by an element a in the group G De ne an isomorphism between two groups De ne a homomorphism between two groups Things you should know how to show Maps 7 show a map is inj ective surjective or bijective Find the image and or preimage of a set under a map Compose two maps Binary Operations Show an operation is associative or commutative Find an identity for an operation Find inverses for an element under an operation Show an operation is closed on a particular set Use the Euclidean algorithm to nd a gcd and write it as a linear combination of the elements a and b Perform arithmetic in Zn Prove or disprove that a set with a binary operation is a group Prove or disprove that a subset of a group is a subset Describe the cyclic group generated by a particular element of a group Decide whether a map is a homomorphism or an isomorphism Things you should be able to prove A relation is or is not an equivalence relation Basic properties of integers Proof by induction and complete induction Properties of divisors and multiples Prove a set is a group Prove a subset is a subgroup Text Problems to try Disclaimer 7 There are A LOT of problems on this list you should not do them all but you should read them all and ask yourself What techniques are needed to answer this question or Do I know what to do for this question Review Problems Section Problems 12 3 4 9 15 14 1210 15 1 2 16 20all 25 26 17 2 9 10 21 2 9 10 22 13 14 44 23 91719 23 35 24 3a 4 14 25 3 5 25 26 26 1 3 5 31 1102126 32 1 2 3 33 7 8 21 34 3 12 35 1 3 Studying for the midterm 1 Do the homework on chapter 3 2 Look at the solutions to the homeworks on the web do you see what I did 3 Learn the de nitions 4 Be in class Monday for reView and hands on practice 5 Try some of these reView problems maybe one per section 6 Read all the reView problems What kinds of questions are these I will be available Monday afternoon from 230 7 4 for extra questions


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