| MTH316: Algebra |
Instructor: Tom Sharland
Course description: This is an introductory course in abstract algebra and more precisely on group theory. Starting from the definitions, we will prove a number of fundamental results about these algebraic structures. There will be an emphasis on proofs in this course, so some mathematical maturity will be expected.
This course will be relatively fast-paced, so in order to keep up with the material, you should be prepared to spend sufficient time outside of class attempting practice problems and reading and understanding your notes and textbook.
Textbook: Contemporary Abstract Algebra (9th ed.) by Joseph A. Gallian. If you happen to have the 8th edition, this should be fine - I will try to accommodate any differences when setting homework. The author has a webpage dedicated to the book, you can find it by following this link. The second, third and fourth items are particularly enlightening and well worth reading.
Prerequisites: MTH 215 and MTH 307.
Homework and Quizzes: Homework will be assigned weekly and will contain two components. Each week I will highlight in bold font three questions, one of which (your choice) should be carefully solved and handed in at the start of class on the following Tuesday - this is the first component. You are expected to produce legible, well argued answers with full explanations. The second component will be weekly quizzes (no notes allowed) which will be based on (but not necessarily exactly the same as) the questions in the homework. Some leeway will be given on these answers due to time constraints. Each component will contribute half-weight to the total homework score, thus each is worth 10% of the total grade.
Knowledge Check:To make sure you are keeping on top of the material, I will carry out a weekly knowledge check. This will be a short test where you are required to write down a definition or a result from class. Knowledge of these are vital for success in this class - if you don't know what the terms mean, you won't be able to prove results about them!You are also expected to keep up with the reading to maintain pace with the class. I will post suggested reading each week. Note that mathematical reading is different from reading a novel or magazine: you will need to concentrate on the exact words and phrases, and probably use a pen/cil and paper to verify some of the claims made for yourself. The textbook is designed to complement your notes, so take advantage of both!
Grade breakdown: The grading scheme will be as follows: