Advanced Algebra for Secondary Ed Teachers
GENERAL EDUCATION: This course does not fulfill a General Education requirement.

CATALOG DESCRIPTION: This course is for secondary education majors and minors. The course takes many of the topics taught in high school or junior high school math classes and treats those topics from a more advanced standpoint. This course is for secondary education majors and minors. In addition topics from linear algebra as they relate to teaching in the secondary schools will be addressed. (Fall)
DESCRIPTION: This course will link many of the common ideas found in elementary algebra classes and show direct connections upon which these ideas originate using the theory of groups, integral domains, and fields, as well as, other topics commonly found in an elementary abstract algebra course.

The teacher candidate will be exposed to certain topics in Linear Algebra that will be directly linked to subject matter taught in their future classroom. Such topics include matrices, operations involving matrices, finding inverse matrices, solving systems of equations using matrices, and study in the theory of linear transformation.

There will be discussion on the algebraic and geometric properties of the trigonometric functions from a more advanced point of view than the teacher candidate will have been exposed to.
TOPICS: Topics discussed in this course are those encountered in traditional algebra classes however, from a more advanced point of view. Topics to be included are: Real and Complex Numbers, function analysis, theory of equations, equality, equivalence, isomorphism, mathematical induction, divisibility properties, modular arithmetic, Archimedean and complete ordered fields.
OBJECTIVES: The teacher candidates will understand the theoretical foundations upon which many of the math courses they will be teaching have evolved. they will be able to answer the questions posed by inquisitive students such as, "Why is (-1)(-1)=+1 or, Why is 0x=0?" The teacher candidate in this class will be able to answer these questions and many other like them by using correct mathematical reasoning, rather than responding with, "Well, that's just the way it is."
REQUIREMENTS: The teacher candidate enrolled in this course will be required to study the course textbook and present his understanding of the subject matter to other members of the class. The candidate will be required to solve or prove mathematical problems and propositions, sometimes alone, and at times in a group setting. The candidate will be required to do assigned readings, homework, oral and written reports, take exams, and collaborate on class projects.
OTHER: This course will have variable credit. Students registered for two credits will attend for one-half the semester and will be assessed for the work required during that time period. Students registering for four credits will attend the class the entire semester. All math majors must register for Math 440 (four credits). Any math minor prepared to begin their math course work with Math 112 (Calculus) must also register for Math 440 (four credits). Any student desiring a math minor and not prepared to begin their math course work with Math 112, first take Math 111, a two-credit prerequisite. Students in this situation must then register for Math 440 for two credits. This must be done so as to adhere to the university's policy of not allowing "hidden" prerequisites.