  
Student Learning Outcomes 
 Students will apply Polya’s problemsolving method to solve problems from a variety of qualitative contexts. They will select, construct, and use mathematical models, identifying salient features of particular phenomena and interpreting and justifying the reasonableness of their results.
 Students will develop conceptual understanding of Polya’s problemsolving method. They will demonstrate this understanding by communicating/presenting their thinking on each of the four steps: Understanding, planning, acting, checking.
 Students will investigate particular phenomena analytically, numerically, graphically, and verbally.

Description  
 A survey of mathematical models and other tools to introduce the nonspecialist to the methods of quantitative reasoning. Problem solving by Polya's method with analytic, numeric, graphical, and verbal investigation. Selecting, constructing, and using mathematical models. Interpreting quantitative results in qualitative context. Emphasis on deductive reasoning and formal logic; algebraic, exponential, logarithmic, and trigonometric models; probability and the normal distribution; data analysis; and selected topics from discrete math, finite math, and statistics.


Course Objectives  
 The student will be able to:
 Use Polya's problemsolving method.
 Practice sound logical reasoning and identify common errors in logic.
 Express quantitative ideas in accurate mathematical language and notation.
 Investigate problems analytically, numerically, graphically, and verbally.
 Identify salient quantitative features of particular phenomena.
 Select appropriate mathematical functions to model particular phenomena.
 Construct mathematical models appropriate to given problems.
 Justify the selection and construction of a particular mathematical model.
 Use mathematical models accurately.
 Interpret the output of a mathematical model in qualitative context.
 Justify the reasonableness of a mathematical outcome in qualitative context.

Special Facilities and/or Equipment  
  Graphing calculator
 When taught hybrid: Four lecture hours per week in facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  A Brief History of Mathematics
 Early Mathematics
 Contributions From Different Cultures
 Review of Basic Mathematical Concepts
 Basic Rules
 Percentages
 Prime Numbers and Factorization
 Greatest Common Factor
 Rationals and Irrationals
 Binary Arithmetic
 Applications of Powers and Geometric Sequences
 Applications of Powers
 Halflives
 Compound Interest
 IRA's/Annuities?Present and Future Value
 Geometric Series
 Areas and Volumes
 Areas
 Volumes
 Surface Area of a Solid
 Galilean Relativity
 Displacement and Velocity Vectors
 Doppler Effect
 Components of Vectors
 Special Relativity
 Simultaneity and Einstein's Postulates
 Time Dilation
 Length Contraction
 Probability
 Reasoning with Formal Logic
 Truth Tables
 Entailment
 Converse, Inverse, and Contrapositive
 Counterexamples
 Errors in Logic
 Developing and Using Mathematical Models
 Power Functions and Polynomial Models
 Exponential and Logarithmic Models
 Trigonometric Models of Periodic Phenomena
 Probabilistic Models
 The Normal Distribution
 Other Selected Models
 Choosing Appropriate Mathematical Models
 Polya's Method
 Data Analysis
 Pattern Matching
 Rates of Change
 Other Model Selection Criteria
 Applying Mathematical Models to Selected Applications
 Growth and Decay
 Carbon Dating
 Isotope Storage
 Drug Metabolism
 Time of Death
 Periodic Phenomena
 Hours of Daylight
 Tides
 Temperature Fluctuation
 Orbital Mechanics
 Acoustic Waves
 Electrical Currents
 Logarithmic Scales
 Richter Scale for Earthquake Magnitude
 Decibel Scale for Sound Intensity
 pH scale for Chemical Acidity
 Biological Populations
 Voting and Apportionment Problems
 Financial Applications
 Economic Utility
 Compound Interest
 Present and Future Values
 Depreciation
 Resource Allocation
 Risk Analysis
 Public Health Policies
 Medical DecisionMaking
 Other Applications

Methods of Evaluation  
  Homework
 Class Participation
 Term paper(s)
 Presentation(s)
 Computer Lab Assignment(s)
 Quizzes
 Unit Exam(s)
 Proctored Comprehensive Final Examination

Representative Text(s)  
 Bello, Ignacio, et. al., Topics in Contemporary Mathematics, Houghton Mifflin, Eighth ed., 2005. Aufmann, Richard N., et. al., Mathematical Excursions, Houghton Mifflin, 2004.

Disciplines  
 Mathematics


Method of Instruction  
 Lecture, Discussion, Cooperative learning exercises.


Lab Content  
 Not applicable.


Types and/or Examples of Required Reading, Writing and Outside of Class Assignments  
  Homework Problems: Homework problems covering subject matter from text and related material ranging from 30  60 problems per week.
Students will need to employ critical thinking in order to complete assignments. Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes.Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB. Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class. 