Presents topics in sets, logic, numeration systems, geometric systems, and elementary computer concepts. Lecture 3 hours per week.
GENERAL COURSE PURPOSE
The general purpose of this course is to give the student an appreciation for the uses of mathematics in the contemporary world and to develop ability by the student to solve certain mathematical problems in a logical manner.
ENTRY LEVEL COMPETENCIES
Prerequisites are a satisfactory score on an appropriate proficiency examination and MTH 003 -"Algebra I", MTH 004 - "Algebra II", and geometry or equivalent. MTH 151 and MTH 152 do not have to be taken in sequence.
GENERAL EDUCATION GOALS
I. Students will develop college-level communication skills.
Students will write about and discuss the concepts introduced in this course. They will also learn to present problem solutions so that others can understand their work.
This will happen throughout the course.
Quantitative skills will be developed through such activities as calculations of geometric properties and conversion between different number bases. Computer skills will be developed by using a software package or the Internet.
Students will solve problems dealing with scientific and technological topics throughout the course.
A. perform operations on sets and Venn diagrams and solve problems utilizing set operations
B. analyze a statement for logical structure and truth value
C. discern the validity of arguments
D. demonstrate the relationship between place values and number bases
E. distinguish between Euclidean geometry and non-Euclidean geometry
F. apply topological concepts
G. apply computer concepts
A. Sets1. Set notation
2. Relations-equality, subset, disjoint sets
3. Operations-union, intersection, complement
4. Venn diagrams
5. Applications-survey problems
B. Logic1. Statements
3. Propositions (negation, conditional, converse, inverse, contrapositive)
4. Truth tables
5. Validity of arguments
6. Logical equivalence
C. Numeration Systems1. Historical perspective of numerical systems
2. Place value systemsa. Binary3. Conversion between bases
4. (optional) Computation in bases other than decimal
D. Geometry1. Euclidean geometry – concepts such as area, perimeter, and volume
2. Non-Euclidean geometry
3. Topology – concepts such as genus, networks, tiling, and the four color theorem
E. Computer concepts – required use of one or more of the following:1. Mathematics software package
4. Mathematical applications of the InternetF. Optional topics1. Sequences and Seri
4. Consumer mathematics
5. Metric system
6. Number Theory