Advanced Algebra for Secondary Ed Teachers | |||
TCHRS ADV ALG | |||
CLASS CODE: | MATH 440 | CREDITS: 2 - 4 | |
DIVISION: | PHYSICAL SCIENCE & ENGINEERING | ||
DEPARTMENT: | MATHEMATICS | ||
GENERAL EDUCATION: | This course does not fulfill a General Education requirement. | ||
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. In addition, topics from abstract algebra as they relate to teaching in the secondary schools will be addressed. | ||
TAUGHT: | Fall | ||
CONTENT AND 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. | ||
GOALS AND OBJECTIVES: | 1. Know alternate definitions, language, and approaches to mathematical ideas. 2. Generate extensions and generalizations of familiar theorems. 3. Study the historical contexts in which concepts arose and have changed over time. 4. Analyze common problems of high school mathematics from a deeper mathematical level. 5. Demonstrate alternate ways of approaching problems, including ways with and without calculator and computer technology. 6. Make connections between ideas studied separately in different courses. 7. Apply the ideas of abstract algebra to analyze the structure of various number systems. 8. Practice making conjectures and verifying with proofs. 9. Experience the power of number theory in solving problems with integral domains. 10. Compare Euclidean and non-Euclidean geometries. |
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REQUIREMENTS: | The student will be required to study the course textbook and present his understanding of the subject matter to other members of the class. The student will be required to solve or prove mathematical problems and propositions, sometimes alone, and at times in a group setting. Other requirements will be to do assigned readings, homework, oral and written reports, take exams, and collaborate on class projects. | ||
PREREQUISITES: | Math 301 | ||
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. | ||
EFFECTIVE DATE: | August 2003 |