Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 25


COURSE DESCRIPTION
25 A Survey of Mathematics Units: 3.00
 
Prerequisite(s): MAT 35: Intermediate Algebra
This is a survey course with selected topics from the history and development of mathematics, patterns and inductive reasoning, set theory and deductive reasoning, the real number system, algebra, geometry, probability, statistics, and problem solving. It is designed for students majoring in liberal arts, education or communication. Calculators or computers may be used for selected topics. 54 hours of lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
This course is designed for students majoring in liberal arts, education or communication.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Apply the basic operations of algebra on the set of real numbers.

  2. Solve linear, exponential, and rational equations and system of equations.

  3. Graph basic functions.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

Apply fundamental relations and operations on sets.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Apply fundamental concepts of logic.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Associate mathematical models with real world situations from other disciplines.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Apply statistical methods and interpret results in business and humanities applications.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Consider and evaluate rival hypotheses
  3. Critical Thinking - Recognize and assess evidence from a variety of sources
  4. Critical Thinking - Generalize appropriately from specific contexts
  5. Critical Thinking - Integrate knowledge across a range of contexts
  6. Breadth of Knowledge - Analyze experimental results and draw reasonable conclusions from them
  7. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  8. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Apply permutations, and combinations in statistical applications.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

Integrate historical context with many of the topics in mathematics.
   

  1. Critical Thinking - Integrate knowledge across a range of contexts
  2. Breadth of Knowledge - Understand the basic content and modes of inquiry of the major knowledge fields
 
COURSE CONTENT
  TOPICS
 
  1. Logic: Symbolic logic, truth tables, conditional statements, and analyzing arguments.
  2. Sets and counting: Set and set operations and application of Venn diagrams.
  3. Combinatorics: Permutations and combinations.
  4. Probability.
  5. Statistics: Data, measures of central tendency, measures of dispersion, the normal distribution, and margin of error.
  6. Finance: Simple and compound interest, and annuities.
  7. Historical perspective on selected topics.
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Class lectures, discussions, and demonstrations of the fundamental relations and operations on sets, concepts of logic, mathematical models, permutations, combinations, and statistical methods and applications providing a historical perspective for many of these topics. Delivery of content may take place in an on-line/distance education setting.
  • Drills and pattern practices utilizing handouts and/or computer-based tools in order to assist the students in mastering the techniques involved in the fundamental relations and operations on sets, concepts of logic, mathematical models, permutations, combinations, and statistical methods and applications.  
  • Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computer-based tools, manipulatives, and worksheets in order to address multiple learning styles and to reinforce material.
  • Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problem solving skills.
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • Written homework assignments and/or computerized homework assignments for correct application of the principles as well as the correct use of symbols and vocabulary.
  • Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of the principles of the fundamental relations and operations on sets, concepts of logic, mathematical models, permutations, combinations,  and statistical methods and applications.  
  • Classroom discovery activities for content knowledge and conceptual understanding.
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
COURSE MATERIALS
 All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include:

  • Johnson/Mowry. Mathematics, a Practical Odyssey. 5th ed. Brooks/Cole Publishing Company, 2004.
  • Miller/Heeren/Hornsby. Mathematical Ideas. 10th ed. Addison Wesley Publishing, 2004.
  • Smith, Karl J.. Nature of Mathematics. 11th ed. Thomson Learning, 2006.
  • Pattern blocks, algebra tiles, and other manipulatives
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