MATH 341 Fall 2024
Algebraic Structures I
Charles Cusack
Mathematics and Statistics
Hope College



CSCI 125
CSCI 255
MATH 341


Course Information

Time     9:30-10:50am TR
Location     VanZoeren 299

Instructor     Chuck Cusack
Office     VWF 217B
Phone     395-7271
Office Hours       1:00-1:50 MWF

  • 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.