A Book of Abstract Algebra, Second Edition, Charles Pinter, Dover Press, 1990.
Description
According to the course catalog:
An introduction to algebraic systems including a study of groups, rings, and integral domains.
Topics
See the Schedule for a detailed list of topics.
Course Learning Outcomes:
become proficient with content related to the theory of groups, rings, and fields,
improve mathematical communication skills -- specifically proof construction, mathematical writing, and verbal communication skills
gain maturity in problem solving, mathematical intuition, and abstract mathematical thinking.
Assessed Student Learning Outcomes (Mathematics Major BA/BS):
Proficiency in Algebra
Mathematical Writing
General Education Learning Outcomes:
N/A since this is not a Gen Ed course.
Student Learning Outcomes - Mathematics Secondary Education Content Standards
D.1.1 including elementary number theory and operations with complex numbers.
D.1.1(e): Apply and connect concepts such as factor, prime, divisible, and multiple to particular numbers and sets of numbers.
D.1.3 including algebra from a more theoretical approach such as relationships among groups, rings, and fields and concepts from linear algebra. In particular, D.1.3(acdei) -- students should be able to
Explain how algebra as the language of generalization is useful for describing patterns and relationships.
Describe how algebraic concepts build from arithmetic and are connected to other content areas, such as geometry, statistics, and calculus.
Describe the role of and be able to apply definitions, reasoning and proof in algebra including identifying conditions under which theorems are valid, recognizing contradiction as a proof strategy, and using conjectures to investigate algebraic relationships.
Use different technologies to enhance the learning of mathematics such as computer algebra systems to investigate algebraic structures and to check results; spreadsheets to produce and explore regularity in repeated reasoning; graphs to explore algebraic relationships; and interactive dynamic technologies to develop conceptual understanding of key algebraic topics.
Explain and justify routine procedures involved in manipulating expressions and solving equations including the use of the properties related to multiplication, addition, and equality.
D.1.4(abc)
Recognize the value of function as the language and organizational structure in the analysis of mathematical relationships.
Understand how algebra concepts are related to the ideas of function and that not all algebraic equations are functions.
Represent functions, with and without technology, in a variety of ways including mapping diagrams, function notation, recursive definitions, tables, and graphs.