Discipline: Mathematics
Originator: Janet Frewing

Riverside Community College District
Integrated Course Outline of Record

Mathematics 25
MAT-25 : Mathematics for the Liberal Arts Student
College:
Lecture Hours: 54.000
Outside-of-Class Hours: 108.000
Units: 3.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-35 or MAT-42 or qualifying placement level.
Course Credit Recommendation: Degree Credit

A college level survey course of selected topics from the history and development of mathematics, patterns and inductive reasoning, set theory and deductive reasoning, geometry, probability, statistics, and problem solving. You may cover 2 of the following topics: dimensional analysis, geometry, mathematics of different bases, or development of numerical systems from ancient cultures. 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
A college level course designed for students majoring in liberal arts, education, or communication.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Apply the basic operations of algebra on the set of real numbers.
    • MAT-35 - Simplify algebraic expressions using correct mathematical symbols and language.
    • MAT-35 - Identify and apply appropriate methods to solve rational, radical, exponential, and logarithmic equations.
    • MAT-42 - Apply algebraic principles and techniques to the solution of applications.
    • MAT-42 - Simplify numerical, algebraic and linear expressions using correct mathematical symbols and language.
  2. Solve linear, exponential, and rational equations and system of equations.
    • MAT-35 - Solve applications that require writing and solving equations. Communicate solution in the context of the problem.
    • MAT-42 - Apply and identify appropriate methods to solve linear equations, quadratics equations, literal equations and inequalities in one and two variables.
  3. Graph basic functions.
    • MAT-35 - Graph linear and basic nonlinear functions.
    • MAT-42 - Graph linear and basic non linear functions (by hand and using technology)
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Use inductive and deductive reasoning to predict patterns or sequences and prove conjectures
  2. Use problem solving techniques to solve real word application problems in a step by step format.
  3. Solve real life application problems using set operations and Venn diagrams
  4. Determine the validity of symbolic and syllogistic arguments
  5. Solve application problems using area, volume, surface area and the Pythagorean theorem. Demonstrate the ability to perform dimensional analysis within each application problem as needed.
  6. Find angle measurements to solve real life applications.
  7. Construct and analyze transformations of objects in two dimensional space.
  8. Use permutations, combinations, compound, and conditional probabilities to solve statistical applications.
  9. Integrate historical topics throughout the course to enhance the students understanding of the origins or each topic.
  10. Demonstrate the ability to add, subtract, and multiply quantities in another base. Also, convert a quantity in one base to a quantity in another base.
  11. Discover the development of numerical systems by analyzing the number systems from Pre-historic civilizations, Babylonians, Egyptians, Romans and Hindu-Arabic cultures.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Apply fundamental relations and operations on sets.
  2. Analyze fundamental concepts of formal logic.
  3. Associate mathematical models with real world situations from other disciplines.
    • Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
  4. Apply statistical methods and interpret results in business and humanities applications.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
  5. Apply permutations, and combinations in statistical applications.
    • Critical Thinking: Students will be able to demonstrate higher-order thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
General Education Outcomes:
Course Content:
  1. Critical Thinking/Quantitative Reasoning Skills
    1. Inductive and Deductive reasoning
    2. Problem Solving Techniques
    3. History:  George Polya
  2. Sets
    1. Set Notation
    2. Set Operations:  complement, union, intersection, difference and Cartesian products
    3. Subsets and proper subsets
    4. Equal and Equivalent sets
    5. Venn Diagrams for two and three sets
    6. Finite and Infinite Sets
    7. Solve application problems that involve various types of sets and survey data
    8. History:  Georg Cantor
  3. Logic
    1. Determine if a sentence is a statement
    2. Negation of a statement containing quantifiers (all, some and none)
    3. Truth tables for negation, conjunction, disjunction, conditional and biconditional statements
    4. Compound statements that are logically equivalent to each other
    5. Converse, inverse and contrapositive statement given conditional statement and the logical equivalent
    6. Validity of symbolic argument using Laws of Inference and Proof
    7. Validity of symbolism using Euler Diagrams
    8. History:  Leonhard Euler
  4. Combinatorics:
    1. Difference between the calculations of permutation and combination
    2. Application problems using the different counting principles and selecting between different principles
    3. History: Pascal and DeFermat
  5. Probability
    1. Difference between Empirical probability and theoretical probability
    2. Sample space by using a tree diagram
    3. Counting principles to determine the number of possible outcomes of an event
    4. Compound probability of and event occurring (and/or) with and without replacement 
    5. Difference between mutually exclusive, independent and dependent events.
    6. Conditional probability given two events
  6. Statistics
    1. Mean, median, mode, variance and standard deviation.
    2. Normal distribution, z-score and area under a curve using a table
  7. Finance
    1. Simple and compound interest
    2. Annuities

Substantial Introduction to two of the following topics:

  1. (Optional) Historical perspective on selected topics
    1. The beginning and development of numerical systems.
      1. Pre-history 
      2. Babylonians
      3. Egyptians
      4. Roman
      5. Hindu-Arabic
      6. Indigenous Americans
    2. The use of different algorithms for calculations
      1. Egyptian Multiplication
      2. Russian peasant Multiplication
      3. Lattice Multiplication
  2. (Optional) Mathematics of different bases.
    1. Translate between bases
    2. Addition and multiplication tables for other bases
    3. Arithmetic in other bases
  3. (Optional) Dimensional Analysis
    1. Metric units of length, mass and volume using the prefixes of the metric system
    2. Units of measure within and between the American system and the metric system
  4. (Optional) Geometry
    1. The basics of geometry
    2. Names of angles that are formed by two rays
    3. Difference between vertical, corresponding, alternate interior and alternate exterior angles
    4. Differences between triangles based on their angle measure and side measurements
    5. Application problems involving two dimensional figures: perimeter, area, circumference, Pythagorean theorem
    6. Application problems involving three dimensional figures: volume and surface area 
    7. Transformational Geometry using reflections, translations, reflections and dilutions
    8. Application problems using similar triangles
    9. History: Euclid


Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
  • 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.
  • 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 to promote mathematics discovery, enhance problem solving skills, and communicate mathematical techniques/solutions to others.
  • Computer-assisted, graphics calculators and/or web-enhanced instruction for, but not limited to understanding logic, Venn diagrams, and calculating financial related values.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
  • Individual and group assignments including problem sets, essays, reports, projects, and calculator/computer assignments designed to demonstrate successful understanding and application of basic concepts and definitions in set theory, logic, and probability for the  liberal arts, education or communication fields of study.
  • Quizzes/examinations designed to assess students’ ability to recall, and apply different algorithms required for calculations of statistical results.
  • Participation in class discussions to ensure progress in mastering ancient methods of calculation with integers.
  • Participation in collaborative learning projects and problem sets to demonstrate mastery of logic and other topics.
  • Midterm and final examination designed to assess students’ mastery and ability to devise, organize and present complete solutions to survey of mathematics problems for the liberal arts, education or communication fields of study.
Sample Assignments:
Outside-of-Class Reading Assignments
  • Reading of the textbook, handouts, lecture notes on topics that include and are not limited to logic, statistics, and financial functions.
Outside-of-Class Writing Assignments
  • Problem sets requiring students to present complete solutions to concepts relating to, but not limited to, graph theory, historical algorithms, and Venn diagrams.
Other Outside-of-Class Assignments
  • Review study guides, homework problems, and topic related videos on concepts related to, but not limited to, probability theory, truth table creation, and validation of arguments.
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 the following:
  • Angel, Abbott, and Runde. A Survey of Mathematics. 10th Edition Pearson, 2016.
  • Johnson/Mowry. Mathematics, a Practical Odyssey. 6th Cengage, 2016.
  • Miller/Heeren/Hornsby. Mathematical Ideas. 13th Pearson, 2012.
  • Sobecki, Bluman, Schirck-Matthews. Math in Our World. 4th McGraw-Hill, 2018.
  • The use of pattern blocks, algebra tiles, and other manipulatives to physically represent mathematical concepts.
Codes/Dates:
CB03 TOP Code: 1701.00 - Mathematics, General
CB05 MOV Transfer Status: N/A (not in college inventory) (D)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
Board of Trustees Approval Date: 01/15/2019
COR Rev Date: 01/15/2019