MTH 461: Survey of Modern Algebra
University of Miami, Spring 2026
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: 10am-11am Tuesday, 8am-9am Thursday, or by appointment
Time and Location: TuTh 12:30-1:45pm,
Dooly Memorial 118
Course syllabus can be found here.
Writing assignment (for writing credit): info here.
Homework Assignments
All homeworks are worth the same, even if graded out of different totals.
| Assignment |
Due Date |
Remarks |
| Homework 1: pdf |
1/22/26 |
|
| Homework 2: pdf |
1/30/26 |
|
| Homework 3: pdf |
2/6/26 |
|
| Homework 4: pdf |
2/13/26 |
|
| Homework 5: pdf |
3/3/26 |
|
| Homework 6: pdf |
3/17/26 |
|
| Homework 7: pdf |
3/26/26 |
|
| Homework 8: pdf |
4/9/26 |
|
Course Schedule
| Date |
Lecture Content |
Reading |
| 1/13/26 |
Syllabus overview. Introduction. Definition of a group. |
note 1 |
| 1/15/26 |
Cayley tables. Properties of groups. Solving equations in groups. Subgroups. |
note 2 |
| 1/20/26 |
Integers modulo n. |
note 3 |
| 1/22/26 |
Multiplicative inverses mod n. Euclidean algorithm |
note 4 |
| 1/27/26 |
Orders of elements. Symmetries and groups. |
note 5, note 6 |
| 1/29/26 |
Permutations and Symmetric groups. |
note 7 |
| 2/3/26 |
Even/Odd permutations. Alternating groups. Symmetries of the Tetrahedron. |
note 8 |
| 2/5/26 |
Cosets. Lagrange's Theorem and its consequences. |
note 9, note 10 |
| 2/10/26 |
Application: RSA cryptosystem. |
note 11 |
| 2/12/26 |
Normal subgroups and quotient groups. |
note 12 |
| 2/17/26 |
Practice problems: pdf, Solutions: pdf |
|
| 2/19/26 |
Exam 1 |
pdf |
| 2/24/26 |
Homomorphisms and Isomorphisms. |
note 13 |
| 2/26/26 |
More homomorphisms and Isomorphisms. |
note 15 |
| 3/3/26 |
Complex numbers and groups. |
note 14 |
| 3/5/26 |
First Isomorphism Theorem. Symmetries of a cube. |
note 16, note 17 |
| 3/10/26 |
Spring break |
|
| 3/12/26 |
Spring break |
|
| 3/17/26 |
Cayley's Theorem. Classification of finite groups. |
note 18, note 19 |
| 3/19/26 |
Introduction to rings. |
note 21, note 22 |
| 3/24/26 |
Rings, continued. Homomorphisms, kernels, ideals. |
note 23 |
| 3/26/26 |
Practice problems: pdf, Solutions: pdf |
|
| 3/31/26 |
Exam 2 |
|
| 4/2/26 |
Principal ideals and PIDs. |
note 24, note 25 |
| 4/7/26 |
|
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| 4/9/26 |
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| 4/14/26 |
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| 4/16/26 |
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| 4/21/26 |
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| 4/23/26 |
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