# Math 3360–02 – Foundations of Algebra I

### Spring 2017

Textbook: A. Papantonopoulou — Algebra, Pure & Applied
Lectures: TR 11am–12:20pm in M&C168
Office hours: TR 3:30pm–5pm, and by appointment
Material covered: Chs. 1–3, 0.3.30–38, ch. 4, and chs. 6–7
Grading: During the term, there will be two in-class exams, each taking up an entire class period. Additionally, there will be ten homework assignments, of which five (of your own choosing) may be resubmitted within a week of the original due date. The final grade will be computed according to the following percentages:
 In-class exams: 30% (15% each) Homework: 50% (5% each) Final exam: 20%
The dates of the in-class exams are March 1 and April 12.
Important dates:
 Jan. 18: First day of classes March 10–18: Spring Break April 2: No classes May 8: Last day of classes May 12: Final exam, 1:30pm–4pm
Handouts:
 Syllabus Notes on rotations and quaternions Handout for first in-class exam Notes on finitely generated Abelian groups Handout for second in-class exam
Practise problems: Problems and solutions

Learning outcomes:

Students learn how to think and reason abstractly in the context of algebraic structures, and learn how to write correct and clear mathematical arguments in this context. Concepts to be mastered by the students include, but are not limited to, the following:
• Groups and group homomorphisms;
• Group actions;
• Rings and ring homomorphisms.
Learning assessment: The expected learning outcomes for the course will be assessed through in-class exams and activities, homework assignments and class discussions.
 Schedule Date Material covered Suggested exercises Other 1/18 1.1 1.1: 16, 18, 26 1/23 1.1, 0.3.30–38 0.3: 24 First homework assignment 1/25 1.2, 1.3 1.2: 1, 8, 20; 1.3: 1, 2, 7, 12 1/30 1.3 1.3: 23, 24 Second homework assignment 2/1 1.3, 1.4 1.4: 1, 3, 10(abc) 2/6 1.4 Third homework assignment 2/8 2.1 2.1: 5, 8, 14, 17, 18 2/13 2.2 2.2: 1, 3, 8, 9 Fourth homework assignment 2/15 2.2 & notes 2/20 2.3 2.3: 2, 6, 14, 24 Fifth homework assignment 2/22 2.4 2.4: 1, 2, 7, 20 2/27 2.5 2.5: 4, 15 3/1 First in-class exam 3/6 First in-class exam 3/8 3.1 3.1: 4, 5, 13 March 10–28: Spring Break 3/20 3.1, 3.2, 3.3 3.2: 1, 15, 16 ,17; 3.3: 4, 5, 7, 19 Sixth homework assignment 3/22 Notes 3/27 Notes Seventh homework assignment 3/29 Notes Notes: 1, 2, 3, 4 4/3 4.1 4.1: 10, 18 Eighth homework assignment 4/5 4.2, 4.3 4.2: 1, 9; 4.3: 2, 4, 7 4/10 4.4 4.4: 2, 9, 18 4/12 Second in-class exam 4/17 Second in-class exam Ninth homework assignment 4/19 4.4, 4.5, 4.6 4.5: 6, 9 4/24 4.6 4.6: 2, 12, 16 Tenth homework assignment 4/26 5/1 5/3 5/8 5/12 Final exam, 1:30pm–4pm