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**Perspectives on Natural Systems****Logical Systems**

Logic concepts in computer programming and how they can be used in several application environments. Two hours lecture, two hours lab.

This course provides the mathematical and logical tools for understanding core programming concepts. After beginning with a review of elementary algebraic expressions, Boolean algebra (including logical operations such as “and” and “or”, and relational operators such as “less than” and “greater than”) are then covered. These concepts are then used in programming constructs such as selection and iteration (“looping”). Initially, these mathematical and logical concepts are discussed using language-independent computer algorithms; they are then applied to a variety of software applications, such as a simple high-level programming language, a spreadsheet (such as Microsoft Excel) and HTML (the language used for web programming).

N/A (100-level course).

- Attend classroom lectures and course laboratory sessions.
- Complete readings, exams, quizzes, laboratory exercises and homework assignments.
- Demonstrate a working knowledge of course objectives through satisfactory performance on quizzes, exams, laboratory exercises and homework assignments.
- Properly document solutions as specified in laboratory exercises and homework assignments.

MA102 with a grade of 'CR' or MA095 with a grade of 'C' or higher or ACT math score of 18-20 with MA095 placement score of 14 or higher or ACT math score of 21 or higher.

None.

3

**Perspectives on Natural Systems****Logical Systems**

A sampling of topics which mixes mathematics history, its mathematicians, and its problems with a variety of real-life applications.

- Hand Calculators
- Set Theory
- Logic and Proofs
- Computers and Systems of Numeration
- The Real Number System
- Algebraic Models
- Geometry and Trigonometry
- Consumer Mathematics
- Counting Methods and Probability
- Statistics

The course will attempt to make mathematics informative and practical and will stimulate the creativity of the liberal arts student. While the topics will be presented in a straightforward and interesting manner, thought and activity on the part of the student will be necessary. The course is designed for liberal arts students, not for students planning to study advanced mathematics.

The course is taught in a lecture-discussion setting with topics, applications, and problems being the focus of the discussion. Problems from the textbook will be assigned. Reading and written assignments will also be made.

Students are expected to attend all class meetings, participate in discussions, complete reading and written assignments, solve assigned problems, and perform satisfactorily on quizzes and examinations.

There will be at least three one-hour examinations and a final examination. A number of shorter quizzes may also be given.

Credit for MA101/102 and a passing score on the Intermediate Algebra Assessment, MA 095 with a grade of 'C' or higher, or ACT Math subscore of 18-20 with MA 095 placement score of 14 or higher, or ACT Math subscore of 21 or higher.

None.

3

**Perspectives on Natural Systems****Logical Systems**

Real numbers and their operations, properties, and applications, number theory, numeration systems, algebraic properties, graphing, statistics, probability and their historical importance. (General Education course) (4)

This course satisfies the Logical Systems requirement of the General Education Program and meets the first mathematics course requirement in any PK-9 teacher education degree program. The primary objectives are to: Identify and use problem solving strategies. Describe and distinguish among the various number systems, including historical perspectives. Define the four fundamental operations on real numbers in terms of sets, describe and model the conceptualizations of each operation, and describe multiple algorithms for each operation. Describe numbers based on their properties, perform divisibility tests, and find greatest common factors and least common multiples of at least two numbers. Identify different aspects of the philosophy, history, cultural significance and nature of mathematics illustrated in the PK-9 curriculum. Apply numerical methods to the study of probability and descriptive statistics

Students will be able to create a word problem for each of the four basic non-negative rational number operations along with appropriate representation (model) for each. Students will be able to identify and write a remediation plan for a student error pattern involving rational number operations. Students will be able to convert between and operate in different numeration systems.

Students will be expected to contribute to class discussions, to work problems in and out of class, to take all quizzes and tests and to do the outside assignments.

Declared education major in elementary, early childhood, exceptional child, middle school, or human environmental studies: child development option major. ACT Math subscore of 15 or higher or MA050 with a grade of 'NDC' or higher or MA 102 with a grade of ‘C’ or higher or a required score on an appropriate COMPASS placement test. Students with an ACT Math sub score below 22 will co-enroll in MA018.

None.

4

**Perspectives on Natural Systems****Logical Systems**

Functions and graphs, polynomial and rational functions, exponential and logarithmic functions, and sequences. (General Education course)

This distribution is based on 50-minute periods, and is adjusted appropriately for
other formats.

Linear Inequalities in One Variable / Interval Notation (1 day)

Cartesian Coordinate Systems, Linear Equations, Slope (2 days)

Graphing Lines (Parallel/Perpendicular Lines)/Midpoint of a Line Segment (2 days)

Functions, Domain/Range (2 days)

Linear Inequalities in Two Variables (1.5 day)

Systems of Linear Equations and Applications (2 days)

Rules for Whole Number Exponents (2 days)

Polynomial Addition/Subtraction/Multiplication (2 days)

Factoring (Solving Quadratic/Cubic Equations by Factoring) (2 days)

Radicals (nth roots, simplifying expressions, addition, subtraction, multiplication,
division) (3 days)

Complex Number Arithmetic (1 day)

Completing the Square (1 day)

Quadratic Formula (1 day)

Distance Formula/Pythagorean Theorem/Applications of Quadratics (1 day)

Graphs of Quadratic and Cubic Functions (Domain/Range) (2 days)

Polynomial Division (1.5 days)

Zeros of Polynomials (1.5 days)

Graphs of Polynomial Functions (Intercepts, Zeros, End-Behavior, Transformations)
(2 days)

Increasing/Decreasing/Average Rate of Change (1 day)

Rational Expressions and Equations (3 days)

Rational Functions (Domain/Range) (1.5 day)

Graphing Rational Functions (Transformations, 1/x) (3 days)

Polynomial/Rational/Absolute Value Inequalities (3 days)

Radicals (Negative/Rational Exponents, Exponent Rules) (2 day)

Radical Functions (2 days)

Solving Radical Equations (2 days)

Graphing Radical Functions (Domain/Range, Transformations) (2 days)

Piecewise Functions (including Absolute Value) (2 days)

Function Composition (1 days)

Function Inverses (2 days)

Exponential/Logarithmic Functions (3 days)

Solving Exponential/Logarithmic Equations (2 days)

Graphing Exponential/Logarithmic Functions (Domain/Range, Transformations) (2 days)

Sequences and Series (Arithmetic, Geometric) (4 days)

Conics (Circles, Ellipses, Hyperbolas) (4 days)

Review for Final (1 day)

In-Class Examinations (4) (4 days)

Students are required to use graphing calculators in this course.

The course is included in the logical systems category of the General Education program. The primary purposes of the course are to develop problem-solving capabilities requiring a logical structure and to provide the essential algebraic background for work in other fields or courses. The students will be given problems in many disciplines that use algebra in their solutions, thus giving insights into the importance of mathematical skills in almost all aspects of society. Whenever possible the historical development of a problem and its resulting solution will be discussed, and the students will be shown how continued mathematical progress is still affecting modern technology. This course also includes instruction and problems on the intermediate algebra skills necessary to successful completion of the College Algebra portion of this course.

- Attend Class
- Participate in classroom activities
- Provide and use a graphing calculator
- Do homework
- Pass quizzes and tests

Minimum ACT score of 19.

None.

5

**Perspectives on Natural Systems****Logical Systems**

Functions and graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations and inequalities, binomial theorem.

- Functions and Graphs
- Polynomial and Rational Functions
- Exponential and Logarithmic Functions
- The Conics
- Sequences and Series

The primary purposes of College Algebra are to develop problem-solving capabilities that follow logical patterns and to provide the essential algebraic background for work in other fields or courses. The main mathematical topics in this course are functions and graphs, polynomial and rational functions, exponential and logarithmic functions, conic sections, sequences, and series. The historical development of these topics, as well as applications to life and culture, will receive emphasis where appropriate.

College Algebra is taught in a lecture setting. However, there is much interaction between students and the teacher through examples and problems, worked and presented in class. The teacher presents situations to the students that require reasoning intended to produce better problem-solving skills. Problem sets in the textbook constitute the main source of assignments to be completed outside of class, but the students may be asked to complete reading assignments from sources other than the textbook, write on topics of a mathematical nature related to the history of the solution of a particular problem, or use computer based programs to develop solutions to problems.

Students are expected to provide and use a graphing calculator (similar to the TI83), to participate in class discussions, and to work problems both in and out of class. Normally at least 2 hours of work is needed to complete each class assignment. Performance on scheduled tests constitutes the major part of the course grade.

Credit for MA101/102 and a passing score on the Intermediate Algebra Assessment, MA 095 with a grade of 'C' or higher, or ACT Math subscore of 18-20 with MA 095 placement score of 14 or higher, or ACT Math subscore of 21 or higher.

None.

3

** ****&**

In-depth study of polynomial, rational, exponential, and logarithmic and trigonometric functions and equations with applications. Credit may not be received for MA 137 and any of the following: MA133, MA134 or MA 135.

The primary purposes of Precalculus are to develop problem-solving capabilities that follow logical patterns and to provide the essential algebraic and trigonometric background for work in science and technology fields and prepare students for a first semester science and engineering calculus course. The main mathematical topics in this course are functions and graphs, polynomial and rational functions, exponential and logarithmic functions, sequences and series, systems of linear and non-linear equations, and trigonometric relations and identities. The historical development of these topics, as well as applications to real-life situations, will be emphasized in the course. The students will work problems from the problem sets in the textbook as well as other problems presented by the instructor. Students will be encouraged to use technology in the form of graphing calculators and the internet to find information on the history or the solution of a particular problem.

- Attend classes.
- Participate in classroom activities.
- Complete assigned homework.
- Satisfactory performance on quizzes and tests.

MA 102 or MA 106 with a grade of CR; or MA 095 with a minimum grade of C; or ACT Math subscore of 22 or higher.

5

** ****&**

Course will introduce statistical ideas to students. The student will reach an understanding of these statistical ideas, be able to deal critically with statistical arguments, and gain an understanding of the impact of statistical ideas on public policy and in other areas of academic study.

ACT Math subscore of 15 or higher or MA 050 with a grade of 'NDC' or higher or MA 102 with a grade of 'C' or higher or a required score on an appropriate mathematics placement test. Students with an ACT Math subscore below 22 will co-enroll in MA 055

3

**Perspectives on Natural Systems****Logical Systems**

A formal study of argument and inference, emphasizing the application of symbolic techniques to ordinary language.

Logic is the science of argument and inference. Logic allows one to distinguish good inferences (those that reasonable people ought to accept) from bad inferences (those that reasonable people ought to reject). This course focuses on one important subset of inferences, deductive inferences. The course introduces the concept of deductive validity and then develops techniques for determining whether a particular argument is valid. A good deal of time is spent developing a formal machinery for argument analysis. Techniques for translating ordinary language arguments into the formal machinery are developed at length.

Some of the topics to be covered include:

- Language, Logic and Argument
- Recognizing arguments
- Analyzing arguments
- Deductive Validity
- Propositional logic
- Syllogistic logic
- Predicate (relational) logic
- Inductive Reasoning
- Probabilistic reasoning
- Analogical reasoning
- Deontic Reasoning
- History of moral reasoning
- Moral reasoning formalized
- Legal reasoning

This course is geared toward the development of formal techniques and methods for the application of those techniques to ordinary language. Heavy emphasis is placed on skill development and on understanding central logical concepts. Accordingly, class sessions are a mix of lecture-discussions and Socratic examination of students. Exercises are frequently completed in class, with students being called upon both for answers and for explanations of their answers. Students should be prepared to devote 5 (five) hours per week of study time to this course.

- Regular class attendance (be prepared to be called on in class).
- Maintain a Logic notebook.
- Complete routine homework assignments (25% of class grade).
- Three hourly examinations (objective, problem-solving, short essay). (50% of class grade to be determined on basis of exam performance).
- Comprehensive final examination (25% of class grade).

None.

None.

3

Contact

**573.651.2207**

generaleducation@semo.edu

Academic Hall 132

One University Plaza, MS 3400

Cape Girardeau, Missouri 63701