Course Syllabus

Department of Mathematics and Computer Science, Lincoln University

 COURSE ID: MAT-325 COURSE NAME: Modern Algebra I CREDITS: 3

TEXT BOOK:

Fraleigh, John B. (2002) A First Course in Abstract Algebra (7th Edition) Pearson Education.

INSTRUCTOR INFORMATION:

***To be provided for each section***

COURSE DESCRIPTION:

This is the first course in a 2 semester sequence. The following topics will be covered in these courses: set theory, functions and mappings, permutations, theory of groups, rings and ideals, homomorphisms, integral domains, equivalence classes, residue classes, fields, modules.

PREREQUISITE:         MAT-220 (Set Theory and Logic) and MAT-221 (Calculus III)

COURSE GOALS- STUDENT LEARNER OUTCOMES:

The student should
• Axiomatically define binary operations and identify and apply properties of sets with binary operations.
• Verify defining properties of groups for subsets of integers with modular operations.
• Solve problems involving standard groups such as cyclic groups, symmetric groups, groups with modular operations, group of units, and groups of matrices.
• Find all the subgroups of finite cyclic groups.
• Correlate symmetric groups and regular polygons and apply this to game theory.
• Prove propositions involving groups.
• Learn coset decomposition of a group and prove Lagrange's theorem with application to number theory.

TENTATIVE SCHEDULE OF WEEKLY ASSIGNMENTS:

CH 1: (Weeks 1 to 6 )
Section 1: Introduction.
Section 2: Binary Operations.
Section 3: Isomorphic Binary Structure.
Section 4: Groups
Section 5: Subgroups.
Section 6: Cyclic Groups
Section 7: Generating Sets and Cayley Digraphs.
Test 1 and Test 2

CH 2: (Week 7 to 11)
Section 1: Groups of Permutations
Section 2: Orbits, Cycles, and the Alternating Groups.
Section 3: Cosets and the Theorem of Lagrange.
Section 4: Direct Products and Finitely Generated Abelian Groups.
Test 3

CH 3: (Weeks 12 to 16)
Section 1: Homomorphisms.
Section 2: Factor Groups.
Section 3: Factor-Group Computations and Simple Groups
Section 4: Groups Action on a Set
Section 5: Applications of G-Sets to counting
Test 4

Introduction to Rings (the ring of integers) & Fields (Optional)

COURSE ASSESSMENT- LEARNING OPPORTUNITIES*

• Homework

Daily homework will be given on material covered in class, reviewed the next day, and may be collected and graded on an unannounced basis. On all assignments, all work must be shown for credit.

Students are encouraged to work cooperatively. The objective of group work is to develop individual skills while learning to work effectively as a team, to think and talk about problem solving and the underlying mathematical concepts, and to develop the ability to ask and answer questions as they arise. However, each student is responsible for all the assigned material, in other words, students can work on their together, but should not simply copy work from each other.

Students are encouraged to make regular visits during office hours, to meet in study groups, and to use the Math Lab or the Math Tutors from the School of Natural Sciences.

• Quizzes, Tests and Final Exam

Short quizzes will be given on an unannounced basis. One hour in- class exams will be announced at least a week in advance. A cumulative two hour Final Exam will be given as scheduled by the Registrar. NO CALCULATORS are allowed during quizzes and exams, and all work must be shown for full credit.

• Late Work And Make-Ups: All graded assignments, quizzes and exams must be completed when scheduled. Late assignments or make-up tests or quizzes will only be allowed with official documentation and grades may be lowered. To qualify for a make-up, a student must have notified the professor and rescheduled in a timely manner.

 Participation 20% Tests 60% Final 20%

 A 92-100% A- 88-91% B+ 85-87% B 82-84% B- 78-81% C+ 75-77% C 72-74% C- 68-71% D+ 65-67% D 58-64% F 0-57%

UNIVERSITY POLICY

1) Attendance:

Lincoln University uses the class method of teaching, which assumes that each student has something to contribute and something to gain by attending class. It further assumes that there is much more instruction absorbed in the classroom than can be tested on examinations. Therefore, students are expected to attend all regularly scheduled class meetings and should exhibit good faith in this regard. For the control of absences, the faculty adopted the following regulations:

• Four absences may result in an automatic failure in the course.
• Three tardy arrivals may be counted as one absence.
• Absences will be counted starting with whatever day is specified by the instructor but not later than the deadline for adding or dropping courses.
• In case of illness, death in the family, or other extenuating circumstances, the student must present documented evidence of inability to attend classes to the Vice President for Student Affairs and Enrollment Management. However, in such cases the student is responsible for all work missed during those absences.
• Students representing the University in athletic events or other University sanctioned activities will be excused from class (es) with the responsibility of making up all work and examinations. The Registrar will issue the excused format to the faculty member in charge of the off- or on-campus activity for delivery by the student(s) to their instructors.

Students are responsible for proper conduct and integrity in all of their scholastic work. They must follow a professor's instructions when completing tests, homework, and laboratory reports, and must ask for clarification if the instructions are not clear. In general, students should not give or receive aid when taking exams, or exceed the time limitations specified by the professor. In seeking the truth, in learning to think critically, and in preparing for a life of constructive service, honesty is imperative. Honesty in the classroom and in the preparation of papers is therefore expected of all students. Each student has the responsibility to submit work that is uniquely his or her own. All of this work must be done in accordance with established principles of academic integrity.

An act of academic dishonesty or plagiarism may result in failure for a project or in a course. Plagiarism involves representing another person's ideas or scholarship, including material from the Internet, as your own. Cheating or acts of academic dishonesty include (but are not limited to) fabricating data, tampering with grades, copying, and offering or receiving unauthorized assistance or information.

3) The Student Conduct Code:

Students will be held to the rules and regulations of the Student Conduct Code as described in the Lincoln University Student Handbook. In particular, excessive talking, leaving and reentering class, phones or pagers, or other means of disrupting the class will not be tolerated and students may be asked to leave. Students who constantly disrupt class may be asked to leave permanently and will receive an F.

4) The Core Curriculum Learner Competencies:

All courses offered through the Department of Mathematics and Computer Science require students to meet at least the following out of the 8 Core Curriculum Learner Competencies:

(1) Listen and effectively communicate ideas through written, spoken, and visual means;
(2) Think critically via classifying, analyzing, comparing, contrasting, hypothesizing, synthesizing, extrapolating, and evaluating ideas;

(6) Apply and evaluate quantitative reasoning through the disciplines of mathematics, computational science, laboratory science, selected social sciences and other like-minded approaches that require precision of thought;

(8) Demonstrate positive interpersonal skills by adhering to the principles of freedom, justice, equality, fairness, tolerance, open dialogue and concern for the common good.

Note:

* The instructor of a given section of the course may make some modifications to the evaluation as well as to the rest of the syllabi including but not limited to; the grade weights, number of tests, and test total points.

**The grading scale guideline includes a 2-point flexibility.

Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this page _ last updated 9/10/2007.

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