Difference between revisions of "MAT4233"

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Modern Abstract Algebra (3-0) 3 Credit Hours
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==Modern Abstract Algebra==
  
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==Description==
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[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 4233. Modern Abstract Algebra]. (3-0) 3 Credit Hours.
  
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The objective of this course is to introduce the basic concepts of abstract algebra, look into the interaction of algebraic operations with foundational constructions, such as products of sets and quotient sets, and to develop rigorous skills needed for further study.
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Prerequisites: [[MAT3233]].
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The course will focus on groups and homomorphisms, as well as provide an introduction to other algebraic structures like rings and fields.  
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Basic properties and examples of semigroups, monoids, and groups, detailed study of permutation, dihedral, and congruence groups, cyclic groups, normal subgroups, quotient groups, homomorphism, isomorphism theorems, direct products of groups, rings and fields and their basic properties, ideals, polynomial rings. Generally offered: Spring. Differential Tuition: $150.
  
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==Evaluation==
 
  
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* Midterms and an optional final.
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==Text==
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Charles C. Pinter. [https://store.doverpublications.com/0486474178.html ''A Book of Abstract Algebra.''] (Reprint of 2nd. ed. originally published in 1990) Dover Publications, NY (2010). ISBN-10: 0-486-47417-8.
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==Topics==
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{| class="wikitable sortable"
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! Date !! Sections !! Topics !! Student Learning Outcomes
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1
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1 & 2
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Binary operations on sets.
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2
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3 & 4
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Groups: Definition and elementary properties.
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|-
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3
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5
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Subgroups.
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|-
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4
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7 & 8
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Groups of Permutations. Permutations of finite sets.
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|-
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5
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9 & 10
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Group isomorphisms and orders of elements.
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|-
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6
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---
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Review. First midterm exam.
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|-
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7
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11
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Cyclic groups.
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|-
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8
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13
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Counting cosets.
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|-
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9
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14 & 15
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Homomorphisms and quotient groups.
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* Exam score is the best of final score and midterm average.
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|-
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10
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---
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Review. Second midterm exam.
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* Students will have access to several past exams for practice.
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|-
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11
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16
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The fundamental theorem of homomorphism.
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==Text==
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|-
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J. Gallian, [https://isidore.co/calibre/get/pdf/4975 ''Contemporary abstract algebra''] (8e) Houghton Mifflin
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12
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17
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Rings and ideals.
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|-
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13
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18
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Ring homomorphisms.
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|-
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14
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19 & 20
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Quotient rings and integral domains.
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<!-- |- -->
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<!-- | -->
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<!-- 15 -->
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<!-- || -->
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<!-- 21 & 22 -->
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<!-- || -->
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<!-- The integers. Factorization into primes. -->
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<!-- || -->
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<!-- |- -->
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<!-- | -->
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<!-- 14 -->
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<!-- || -->
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<!-- 23 -->
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<!-- || -->
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<!-- Elements of number theory. -->
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<!-- || -->
  
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==See also==
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|-
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15
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---
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Wrap-up and review. Student Study Day.
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* [https://catalog.utsa.edu/undergraduate/coursedescriptions/mat/ UTSA Undergraduate Mathematics Course Descriptions]
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|-
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|}

Latest revision as of 10:49, 25 March 2023

Modern Abstract Algebra

MAT 4233. Modern Abstract Algebra. (3-0) 3 Credit Hours.

Prerequisites: MAT3233. Basic properties and examples of semigroups, monoids, and groups, detailed study of permutation, dihedral, and congruence groups, cyclic groups, normal subgroups, quotient groups, homomorphism, isomorphism theorems, direct products of groups, rings and fields and their basic properties, ideals, polynomial rings. Generally offered: Spring. Differential Tuition: $150.


Text

Charles C. Pinter. A Book of Abstract Algebra. (Reprint of 2nd. ed. originally published in 1990) Dover Publications, NY (2010). ISBN-10: 0-486-47417-8.

Topics

Date Sections Topics Student Learning Outcomes

1

1 & 2

Binary operations on sets.

2

3 & 4

Groups: Definition and elementary properties.

3

5

Subgroups.

4

7 & 8

Groups of Permutations. Permutations of finite sets.

5

9 & 10

Group isomorphisms and orders of elements.

6

---

Review. First midterm exam.

7

11

Cyclic groups.

8

13

Counting cosets.

9

14 & 15

Homomorphisms and quotient groups.

10

---

Review. Second midterm exam.

11

16

The fundamental theorem of homomorphism.

12

17

Rings and ideals.

13

18

Ring homomorphisms.

14

19 & 20

Quotient rings and integral domains.


15

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Wrap-up and review. Student Study Day.

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