Text: Algebra: Abstract and Concrete by Frederick Goodman.

Available online at LINK

The development of the following understandings will be the primary goal of this course:

  1. Algebra is useful, universal and relevant in everyday life and in K-12 mathematics teaching.

  2. Algebra is a living organism, algebraic tools are developed to enable better understanding of the world around us, and the ability to think abstractly is a valuable asset.

  3. Algebraic properties, rules, and concepts make sense.

  4. Mathematics is a language communicated through specialized vocabulary and symbols used to represent and describe mathematical ideas, generalizations, and relationships.

  5. Symmetry plays a key role in science, math, engineering and culture.


  1. Work hard and regularly. This will be a difficult class. Re-write your notes.

  2. Own the fundamental definitions and main results.

  3. Create, and be familiar with a large inventory of examples. The best way to combat abstractness is to have some concrete examples to play with.

  4. Be willing to seek help. There will be times in this course that you will be frustrated. This is natural. This is not an easy course. Anytime you are learning a difficult new task, you encounter frustration. Don’t let the frustration get you down. Come in and talk with me!

  5. Enjoy! You will be exploring an exciting new world, and will be challenging

  6. your mind. What a wonderful opportunity!


  1. Homeworks, in-class activities 25%

  2. Field Guide 25%

  3. Capstone project 25%

  4. Understandings Exams 25%

Projecte & in-class activities

Half of this class will be “flipped”, that is, each week you will watch 4-6 10 minute video lectures on a particular topic.  Associated to some lecture will be a formative assessment. Throughout the course there will be mini-projects, some in-class and some outside of class; some individual and some in groups. For some of these you will be assessed on your participation (are you actively asking questions? are you sharing your thought processes with others?). For others, the group or individual will hand-in a brief report which will be graded based upon mathematical correctness, completeness, creativity, and depth of understanding.

Field guide

Much of this class deals with new and abstract objects. To help better understand

these objects, you will put together a Field Guide of Abstract Algebra & Applications

The field guide will contain material that helps you understand the new objects that we will encounter. Correct definitions, examples, illustrations, explanations and connections to secondary mathematics should be included. The field guide will be collected twice during the course, and graded on correctness, completeness, and richness.

Capstone Project

Two-thirds of the way through the course, groups of students will choose a topic (either from a list to be provided, or one agreed upon by the instructor) in Algebra to study in more depth. During the last week of class each group will present their topic to the class (either as a formal

lecture, a power points presentation, a discovery-activity for the class, etc).

Understandings Exams

Towards the end of the course there will be a ”take-home” exam that will allow you to ply your newly developed skills and understandings.