# National University

General Course Information for MTH416: Algebraic Structures

 Course: MTH416 - Algebraic Structures Textbook: For the correct edition of the textbook assigned to a specific class, go to: http://www.nutextdirect.com Course Prerequisite(s): Course Description: A look at groups, rings and fields, as well as applications of these systems. Discusses equivalence relations, Lagrange's Theorem, homomorphisms, isomorphisms, Cayley's Theorem and quaternions. Also examines error correcting codes and issues of cryptography. Graphing calculator may be required. Course Learning Outcomes: Discuss sets, subsets, and partitions and equivalence relations. Discuss examples of groups, properties of groups; operations on groups. The nature of orbits, cycles, the alternating group, cyclic groups, abelian groups, cosets and Lagrange's theorem. Discuss homomorphisms, or relationships between groups such as isomorphism and factor groups and Cayley's theorem. Compare rings, integral domains, and fields; structures with two binary operations defined on them. Discuss Fermat's and Euler's theorems. Show how homomorphisms are involved in solving a polynomial equation. Discuss irreducible polynomials and their importance. Explain what is meant by quaternions and the historical significance of their development. Discuss rings and their analogy to the study of homomorphisms. Discuss the concepts of an extension field, and of algebraic elements and of transcendental elements and how these tie together to show that every non-constant polynomial has a zero in some field. Describe some applications of abstract algebra: such as in avoiding problems of round off, in error correcting codes, for classifications of crystals, underlying issues behind public key cryptography. Specified Program Learning Outcomes: BACHELOR OF ARTS IN MATHEMATICS EDUCATION WITH NEVADA SECONDARY LICENSURE Develop fundamental knowledge in geometry Employ a variety of reasoning skills and effective strategies for solving problems both within the discipline of mathematics and in applied settings that include non-routine situations Model real world problems with a variety of algebraic and transcendental functions Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs that are appropriate for the research and study in mathematics Use language and mathematical symbols to communicate mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines MAJOR IN MATHEMATICS Employ a variety of reasoning skills and effective strategies for solving problems both within the discipline of mathematics and in applied settings that include non-routine situations Employ algebra and number theory ideas and tools as a base of a fundamental language of mathematics research and communication Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs that are appropriate for the research and study in mathematics Use language and mathematical symbols to communicate mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines MAJOR IN MATHEMATICS WITH A PRELIMINARY SINGLE SUBJECT TEACHING CREDENTIAL (CALIFORNIA) Employ a variety of reasoning skills and effective strategies for solving problems both within the discipline of mathematics and in applied settings that include non-routine situations Employ algebra and number theory ideas and tools as a base of a fundamental language of mathematics research and communication Model real world problems with a variety of algebraic and transcendental functions Use language and mathematical symbols to communicate mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines

Students with Disabilities:
Students seeking special accommodations due to a disability must submit an application with supporting documentation, as explained under this subject heading in the General Catalog. Instructors are required to provide such accommodations if they receive written notification from the University.

Writing Across the Curriculum:
Students are expected to demonstrate writing skills in describing, analyzing and evaluating ideas and experiences. Written reports and research papers must follow specific standards regarding citations of an author's work within the text and references at the end of the paper. Students are encouraged to use the services of the University's Writing Center when preparing materials.

The following website provides information on APA, MLA, and other writing and citation styles that may be required for term papers and the like: http://nu.libguides.com/citations

National University Library:
National University Library supports academic rigor and student academic success by providing access to scholarly books and journals both electronically and in hard copy. Print materials may be accessed at the Library in San Diego or through document delivery for online and regional students. Librarians are available to provide training, reference assistance, and mentoring at the San Diego Library and virtually for online or regional students. Please take advantage of Library resources:

Contact the Library:

• RefDesk@nu.edu
• (858) 541-7900 (direct line)
• 1-866-NU ACCESS x7900 (toll free)

Use the Library Training Tools (on the Library Homepage) for additional help

• Recorded class presentations
• Tutorials & Guides (APA/MLA, Peer-Review, and more)

Plagiarism:
Plagiarism is the presentation of someone else's ideas or work as one's own. Students must give credit for any information that is not either the result of original research or common knowledge. If a student borrows ideas or information from another author, he/she must acknowledge the author in the body of the text and on the reference page. Students found plagiarizing are subject to the penalties outlined in the Policies and Procedures section of the University Catalog, which may include a failing grade for the work in question or for the entire course. The following is one of many websites that provide helpful information concerning plagiarism for both students and faculty: http://www.indiana.edu/~wts/pamphlets/plagiarism.shtml

Ethics:
Ethical behavior in the classroom is required of every student. The course will identify ethical policies and practices relevant to course topics.

Technology:
Students are expected to be competent in using current technology appropriate for this discipline. Such technology may include word processing, spreadsheet, and presentation software. Use of the internet and e-mail may also be required.

Diversity:
Learning to work with and value diversity is essential in every class. Students are expected to exhibit an appreciation for multinational and gender diversity in the classroom.

Civility:
As a diverse community of learners, students must strive to work together in a setting of civility, tolerance, and respect for each other and for the instructor. Rules of classroom behavior (which apply to online as well as onsite courses) include but are not limited to the following:

• Conflicting opinions among members of a class are to be respected and responded to in a professional manner.
• Side conversations or other distracting behaviors are not to be engaged in during lectures, class discussions or presentations
• There are to be no offensive comments, language, or gestures