II.  ACADEMIC CREDIT:  Three semester hours

 

III.  CATALOG DESCRIPTION:  An introduction to abstract mathematical concepts including:  deductive reasoning, logic, sets, symbolism,terminology, methods of proof, group structure, integers as an integral domain, rational numbers, real numbers, and complex numbers as fields.

 

IV.  PLACE OF THE COURSE IN THE CURRICULUM:  This course is used to help meet the requirements of an undergraduate major in mathematics.  It assumes that the student has college algebra or its equivalent and is a prerequisite for such courses as abstract algebra, real analysis, and complex analysis.

 

V.  COURSE OBJECTIVES:  This course

 

       A.  Enables the student to recognize mathematical structures that are present in God"s creation.

       B.  Provides opportunity for the student to become acquainted with the type of thinking that is inherent in the structure of mathematics.

       C.  Gives practice in learning to read and write using mathematical symbols.

        D.  Introduces the student to many of the basic mathematical terms and vocabulary in the form of precise and complete definitions.

        E.  Enables the student to develop and refine analysis and syntheses skills that are necessary for success in mathematics.

        F.  Provides experience and practice in presenting well organized proofs using the proper definitions and procedures as recognized by the international mathematical community. 

   

VI.    STUDENT OUTCOMES:  Upon successful completion of this course, the student should be able to:

 

          A.  Use basic logical connectives and symbolism to convert between statements in English and those in logic.

          B.  Simplify complex logical statements. 

          C.  Use set operations and symbolism to analyze and sijplify problems.

          D.  Identify different relations and functions, using correct terminology, then define and apply them.

          E.   Identify and use isomorphisms between Boolean algebra, sets, logic, and wiring diagrams.

          F.  List and use the properties of the rational numbers and use them to verify attributes  endemic to this field.

          G.  List and use the properties of the integers and use them in simple proofs, including proof by mathematical induction.

          H.  List and use the properties of the real numbers and provide examples of their differences from the rational numbers and integers.

           I.  List and use the properties of the complex numbers and provide examples of their differences from the real numbers.

           J.  Demonstrate the isomorphism between the field of complex numbers, both using the Cartesian plane and the polar plane, including De Moivre's theorem and two dimensional vectors.

 

VII.   LEARNING RESOURCES:

 

         You will need the text:  Structure of Mathematics by Larry Matthews

 

VIII.  EVALUATION:

         Learning will be measured using assignments and exams. Show and organize your work. Including the final exam. there will be 4 exams which will count for 80% of your grade and assignments which will count for the other 20%.  Grading will be on the standard 90%- A, 80%-B, 70%-C, 60%-D, and below 60% failing scale.