# Math 301

(Last updated Saturday, September 30, 2023 @ 2:20pm)

## Course Information and Materials

Instructor: Professor Nicholas Vlamis

Instructor Office: 507 Kiely

Instructor Email: nicholas.vlamis@qc.cuny.edu

Class Meeting: Monday/Wednesday 1:40–3:30pm in Kiely 320

Office Hour: Monday 12–1pm and Wednesday 11am–12pm (or by appointment)

Textbook: Abstract Algebra by Thomas W. Judson, 2021 Edition (pdf | html)

Contact: You can always reach me via email or on Discord. I will try to respond within 24 hours.

Overleaf: an online version of LaTex, which is a mark-up language for writing mathematics (or any document once you become a convert). You can also run LaTex natively on your computer. I'm a Mac user, so I can point you to MacTex, but there are also options for Windows or Linux. I really enjoyed writing homework in LaTeX when I was a student, and I really do think made me a better student.

## Week 5 (Week of September 25)

Suggested reading: Section 3.3

There was no class on Monday, September 25: CUNY was closed.

Exam 1 will be held in class on Wednesday, October 4. The exam will cover all material covered in class from Week 1 through Week 5. In the book, this corresponds to sections 2.1, 2.2, 3.1, 3.2, and 3.3. For homework assignments, this corresponds to Homework Assignments 1, 2, 3, and 4. Remember the majority of exam questions (on the order of 80%) will either be taken directly from a homework assignment or be slight variations on such problems. You may bring one sheet of notes that contains definitions and theorem statements, but nothing else.

Homework Assignment #4. Due Wednesday, October 11. (**Note: the due date is the week after Exam 1; however, the content on the assignment is fair game for the exam.)

Wednesday's class: Introduced the notion of a subgroup, went over subgroup tests, and saw some examples.

## Week 4 (Week of September 18)

Suggested reading: Section 3.2

Monday's class: Worked through constructing several Cayley Tables, including for the set of symmetries of an equilater triangle with respect to function compositons. Defined a group and provided several basic examples.

Wednesday's class: Discuseed examples of groups. Established basic properties of groups.

## Week 3 (Week of September 11)

Suggested reading: Section 3.1

Monday's class: Proved that every natural number is a product of prime numbers. Proved there are infinitely many prime numbers (we gave Euclid's proof). Established mathematical induction as a consequence of the well-ordering principle. Worked in groups on two induction problems, the second of which established a more general form of Euclid's lemma.

Wednesday's class: Stated the Fundamental Theorem of Arithmetic. Introduced modular arithmetic and established basic properties.

## Week 2 (Week of September 4)

CUNY was closed on Monday.

Suggested reading: During the first two weeks of class, we will be covering Section 2.1 and Section 2.2 in the textbook, but not in the same order as presented in the book.

Continue working on Homework Assignment #1, whch is due Wednesday, September 13. Make sure you read the Homework Guide, so you know what the expectaton is.

Wednesday's class: Introduced the greatest common divisor. Proved that the GCD exists, is unique, and can be expressed as a linear combination. Established the Euclidean algorithm and discussed how to use the Euclidean algorithm to write the GCD as a linear combination. Introduced the notion of a prime number and proved Euclid's lemma.

## Week 1 (Week of August 28)

Welcome to Math 301! I will update this section with summaries of each of the week's classes plus any additional information.

Suggested reading: During the first two weeks of class, we will be covering Section 2.1 and Section 2.2 in the textbook, but not in the same order as presented in the book.

Monday's class: Worked in groups investigating the definition of a function and the properties of being injective and surjective. We also talked through a problem about matrices and recalled some facts from linear algebra.

Wednesday's class: Introduced the well-ordering principle. Defined what it means for one integer to divide another. Proved the Division Algorithm. Defined quotient and remainder. Worked on the first couple of homework problems in groups.