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Math 151. Principles of Algebra. Spring 2020.

Prerequisites: Math 111 is required. Math 152 or familiarity with matrices is strongly recommended. Math 114 or 116 or 145 would be helpful.

Hours: 4.

Text: Abstract Algebra by John A. Beachy and William D. Blair, 4th edition.

Content: Integers (divisors, primes, congruences), Functions (composition, one-to-one and onto functions, equivalence relations), Groups, Rings, and Fields (definition, basic properties, and important examples), Polynomials (roots, division, factorization).

Catalog Description: Prerequisite: MATH 111. Equivalence relations; groups, cyclic groups, normal sub-groups, and factor groups; rings, ideals, and factor rings; integral domains and polynomial rings; fields and field extensions.

Course goals
Upon completion of this course, students should know/understand:

  1. Definitions and properties of integers related to divisibility, prime numbers, congruences.
  2. Definitions and properties of functions.
  3. The concepts of a relation and an equivalence relation.
  4. Definitions of and operations with matrices.
  5. Definitions and properties of algebraic structures such as groups, rings, and fields.
  6. Properties of polynomial functions related to roots and factorization.

Learning Outcomes
Upon completion of this course, students should be able to do:

  1. Prove some theorems studied in the course. Prove simple corollaries.
  2. Find divisors, gcd, and lcm of numbers; determine whether two numbers are relatively prime.
  3. Determine whether a function is one-to-one and/or onto.
  4. Determine whether a relation is an equivalence relation.
  5. Perform operations with matrices.
  6. Determine whether a set with a given structure is a group; ring; field.
  7. Determine whether a subset of a group/ring/field is a subgroup/ideal/subring/subfield.
  8. Perform operations with polynomials; find roots of polynomials; factor polynomials.

Grading policy: Your grade for the course will be based on your performance on exams and homework (more information on these below). The number of points awarded for these is as follows.

Test 1 30 points
Test 2 30 points
Test 3 30 points
Final exam 60 points
Homework 100 points
Total 250 points

Points earned Letter grade
220-250 A
190-219 B
160-189 C
130-159 D
0-129 F

Exams: There will be three 50 min long tests and one final comprehensive exam. If for any reason you can not take a test at the scheduled time, please let me know as soon as possible, and certainly before the test. See schedule for exam dates.
UPDATE: some tests may be given on-line due to virtual instruction. Details will be posted on Canvas and the schedule page.

Class attendance is strongly encouraged. In addition to new material, important course information will be given in class, sometimes handouts will be given.

There will be weekly homework due Wednesday at the beginning of class (1:00pm), usually covering the material of the preceding week. You may submit up to 3 homeworks late, but no later than Monday of next week, at the beginning of class. This deadline is very firm because I try to return graded papers on Monday. However, if you are seriously sick and unable to work on the homework, please notify me as soon as possible and ask for a longer extension.
UPDATE: some homeworks are now due on another day of the week. Late homeworks can still be submitted, no later than the Monday of the following week.

Extra Help: It is essential not to fall behind, because each class may use the material studied previously. If you have trouble with some material, seek help in the following ways:

If you are having any difficulties, seek help immediately - don't wait until it is too late to recover from falling behind, or failing to understand a concept!
UPDATE: Make use of Canvas discussion and chat, as well as email.

Computers: At California State University, Fresno, computers and communications links to remote resources are recognized as being integral to the education and research experience. Every student is required to have his/her own computer or have other personal access to a workstation (including a modem and a printer) with all the recommended software. The minimum and recommended standards for the workstations and software, which may vary by academic major, are updated periodically and are available from Information Technology ServicesĀ or the Universit Bookstore. In the curriculum and class assignments, students are presumed to have 24-hour access to a computer workstation and the necessary communication links to the University's information resources.

Students with disabilities: upon identifying themselves to the University, students with disabilities will receive necessary accommodation for learning and evaluation. For more information, see http://www.fresnostate.edu/studentaffairs/ssd/.
UPDATE: The SSD office is still open, including their testing center.

Academic honesty: cheating and plagiarism will not be tolerated in this class. For information on the University's policy, see the University Catalog (section Policies and Regulations).

Honor Code: Members of the CSU Fresno academic community adhere to principles of academic integrity and mutual respect while engaged in university work and related activities. You should:

Disruptive Classroom Behavior: student conduct which disrupts the learning process will not be tolerated and may lead to disciplinary action and/or removal from class.

Copyright policy: Copyright laws and fair use policies protect the rights of those who have produced the material. The copy in this course has been provided for private study, scholarship, or research. Other uses may require permission from the copyright holder. The user of this work is responsible for adhering to copyright law of the U.S. (Title 17, U.S. Code). To help you familiarize yourself with copyright and fair use policies, the University encourages you to visit its copyright web page: http://www.fresnostate.edu/home/about/copyright.html. Digital Campus course web sites contains material protected by copyrights held by the instructor, other individuals or institutions. Such material is used for educational purposes in accord with copyright law and/or with permission given by the owners of the original material. You may download one copy of the materials on any single computer for non-commercial, personal, or educational purposes only, provided that you (1) do not modify it, (2) use it only for the duration of this course, and (3) include both this notice and any copyright notice originally included with the material. Beyond this use, no material from the course web site may be copied, reproduced, re-published, uploaded, posted, transmitted, or distributed in any way without the permission of the original copyright holder. The instructor assumes no responsibility for individuals who improperly use copyrighted material placed on the web site.

Subject to Change: This syllabus and schedule are subject to change in the event of extenuating circumstances. If you are absent from class, it is your responsibility to check on announcements made while you were absent.

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This page was last revised on March 14, 2020.

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