In Ma 5a we will discuss the basic theory of groups. We will mostly focus on finite groups. We will learn basic notions (such as groups, subgroups, cosets, quotient groups, homomorphisms, group actions), basic results (such as the isomorphism theorems, Lagrange's theorem, the Orbit-Stabilizer theorem), basic constructions (such as direct and semidirect products) and basic examples (such as cyclic, symmetric and dihedral groups). We will also touch topics such as: Finite abelian groups and their classification, the Sylow theorems and the Jordan-Holder theorem.
Alexander Yom Din
OLGA TAUSSKY AND JOHN TODD INSTRUCTOR IN MATHEMATICS
Office: 284 Sloan
The final grade will consist of 50% Homework, 25% Midterm exam, and 25% Final exam, and will be roughly given following the scale:
A+ > 93 > A > 87 > A- > 83 > B+ > 78 > B > 74 > B- > 70 > C+ > 62 > C > 55:
Homework will be posted on each Friday, and will be due on the next Friday noon. The homework should be submitted to the Ma 5 box on the second level of Sloan 37.
Main textbook: Dummit, D. S. and R.M. Foote, Abstract Algebra, third edition (chapters 1-5 are relevant, and perhaps some of 0 and 6).
Additional textbooks: TBA
A skecthy summary of the lectures (however, I don't guarantee it to be accurate or full).
Set Theoretic Language - very recommended to internalize.
|10/07/16||Homework 01||Homework 01 Solutions|
|10/14/16||Homework 02||Homework 02 Solutions|
|10/21/16||Homework 03||Homework 03 Solutions|
|11/04/16||Homework 04||Homework 04 Solutions|
|11/11/16||Homework 05||Homework 05 Solutions|
|11/18/16||Homework 06||Homework 06 Solutions|
|12/02/16||Homework 07||Homework 07 Solutions|
|NO DUE||Homework 08|
Midterm exam - is handed out at the secretariat (Sloan 253) starting 10/25/16, and is due 10/31/16 at noon (in the Ma5 homework dropbox). It contains 4 questions and the student should spend 5 hours on it. Collaboration is not allowed.