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# Mathematics for Liberal Arts

Course Code: MATH 1234
Faculty: Science & Technology
Department: Mathematics
Credits: 3.0
Semester: 15 weeks
Learning Format: Lecture
Typically Offered: Fall, Summer, Winter
course overview

Mathematics is everywhere. This one semester course for liberal arts students explores mathematics topics in order to improve quantitative reasoning and decision-making in everyday life, as well as to develop an appreciation for the power and beauty of the mathematics that is evident (and not so evident) in the world around us. Topics include: critical thinking and problem solving, percentages and number sense, uses and abuses of statistics, linear and exponential growth, and math in art and music. Good English writing and communications skills are recommended.

### Course Content

1. Attitudes & Aptitudes:  Why Math matters
2. Critical Thinking
3. Problem Solving
4. Units and Measurement
5. Percentage and Ratio
6. Statistical Reasoning
7. Linear vs. Exponential Growth
8. Intro to Modelling

PLUS at least 2  OF THE FOLLOWING (one of which must be Math in Music, Math in Art, or Math in the Sports Science Classroom):

1. Accuracy and Precision
2. Probability
3. Linear and Exponential Modelling
4. Mathematics in Music
5. Math in Art
6. Math in Financial Management
7. Math in the Sports Science Classroom

DOUGLAS COLLEGE SIGNATURE ELEMENTS:

Core Competencies:

1. Oral, written and interpersonal communication:  Students will be expected to participate in class discussions based on readings, and to submit written assignments in the form of short answers to math problems, short paragraphs, summaries and essays.  A short oral presentation is also a component of the course evaluation.
1. Computational and Information Technology:  Clear and correct mathematical computations are a major component of this course.  Students will be expected to use calculators and spreadsheets effectively.
1. Critical and Creative Thinking:  A unit on critical thinking sets the stage for the rest of the course.  Homework assignments and group discussions involve analysis of quantitative information in order to inform decision-making throughout all units.
1. Teamwork:  Regular group activities in class will promote teamwork.

1. Applied Skills (field, laboratory practicum):  Students will improve and develop skills in practical mathematical computations and critical thinking in order to analyze quantitative data as it appears in the media.  The Math in the Sports Science Classroom unit teaches skills specific to Sports Science educators.  These include tournament design, performance tracking and using a spreadsheet for student grades.
1. Ethical behaviour and social responsibility:  A wide variety of ethical and social issues are addressed in this course as they provide a context for the quantitative arguments that are studied.  Uses and abuses of percentages and other statistics are discussed.
1. Intercultural, International and Global Perspective:  Cultural differences are discussed in the unit on attitudes towards mathematics.  Quantitative reasoning is applied to issues of global concern including population growth, global warming and energy consumption.

### Methods of Instruction

• Lecture
• Discussion groups
• Group activities

### Means of Assessment

Evaluation will be carried out in accordance with Douglas College policy. The instructor will present a written course outline with specific evaluation criteria at the beginning of the semester. Assessments will be taken from the following options:

 Homework 0-20% Term tests 30-60% Quizzes 0-20% Participation/In-class assignments 10-20% Term portfolio project 0-30% Term paper 0-20% Final exam 0-30%

The following is presented as an example assessment format for this course:

 Quizzes/Homework 10% Term test I 15% Term test II 15% Participation/In-class assignments 15% Portfolio project 20% Oral presentation 5% Final exam 20% 100%

### Learning Outcomes

At the conclusion of this course students will be able to:

• identify and discuss at least three common misconceptions about mathematics
• understand and explain the importance of mathematical literacy in modern society
• reflect on the role that mathematics plays in their own lives
• recognize and analyze fallacies in given arguments
• use appropriate logic notation and simple truth tables to analyze the truth values of propositions   involving negation, conjunctions, disjunctions, conditionals
• distinguish between inclusive and exclusive uses of the word “or”
• given a conditional, write its converse, its inverse and its contrapositive
• illustrate relationships between sets using Venn diagrams
• solve problems using Venn diagrams to organize information
• use Venn diagrams to test the validity of arguments
• distinguish between inductive and deductive arguments
• apply critical thinking strategies to analyze arguments
• know standard metric units of measurement
• perform unit conversions
• apply problem solving strategies to solve word problems
• solve percentage problems
• calculate absolute and relative change
• identify common abuses of percentages
• write and interpret numbers in scientific notation
• demonstrate number sense through estimation, comparison and scaling
• understand and give examples of Simpson’s Paradox
• understand and interpret the 5 basic steps in a statistical study
• describe simple random sampling, systematic sampling, convenience sampling and stratified sampling
• distinguish between observational studies and experiments
• describe the placebo effect and the importance of blinding in experiments
• determine a confidence interval from a margin of error
• understand and apply guidelines for evaluating a statistical study
• interpret and create frequency tables, bar graphs, pie charts, histograms and line charts
• interpret graphs that relay statistical information
• distinguish between causation and correlation
• describe possible explanations for correlation
• understand and apply guidelines for recognizing causality
• explain the difference between linear and exponential growth
• calculate the doubling-time or half-life in given situations
• contrast exponential growth and logistic growth
• understand factors affecting carrying capacity
• understand and use the Richter scale, decibel scale, and pH scale
• understand the concept of a mathematical function
• given a real-life functional situation, identify dependent and independent variables, domain and range
• represent functions with tables, graphs and equations
• use functions given in the form of tables, graphs or equations to answer questions about real-life quantities

Depending on the sections covered by the instructor the students will also be able to:

ACCURACY AND PRECISION

• distinguish significant digits from non-significant zeros
• identify and distinguish between random and systematic errors
• calculate absolute and relative error
• distinguish between accuracy and precision
• apply rounding rules for combining approximate numbers

PROBABILITY AND COUNTING

• distinguish between theoretical, empirical and subjective probabilities
• calculate simple probabilities
• make a probability distribution
• calculate probabilities of the conjunction of independent and dependent events
• calculate probabilities of the disjunction of mutually exclusive and non-mutually exclusive events
• understand and apply the law of large numbers
• calculate and interpret expected values
• measure risk in terms of accident or death rates
• understand and interpret vital statistics and life expectancy
• calculate permutations and combinations
• determine the probability of winning a lottery

MORE ADVANCED LINEAR AND EXPONENTIAL MODELS

• calculate the slope of a linear function
• determine the equation of a line
• determine the equation of an exponential function

MATH IN MUSIC

• understand how a plucked string produces sound
• measure frequency and find harmonics of the frequency
• understand the musical scale and the ratios of frequencies among musical notes
• understand how the frequencies of a scale exhibit exponential growth
• explain the difference between analog and digital representations of music

MATH IN ART

• understand the use of perspective in painting
• find symmetries in paintings and tilings
• create tilings with regular or irregular polygons
• name several places that the golden ratio occurs in art and nature

MATH IN FINANCIAL MANAGEMENT

• know when and how to apply formulas for simple interest, compound interest and continuously compounded interest
• understand investment types:  stocks, bonds, cash
• read financial tables for stocks, bonds and mutual funds
• use formulas appropriately to calculate total and annual returns
• understand the uses and dangers of credit cards
• understand considerations in choosing a mortgage
• use the loan payment formula to calculate payments
• calculate the total cost of a loan

MATH IN THE SPORTS SCIENCE CLASSROOM

• solve problems involving energy and power units
• understand and apply the concept of concentration (e.g. blood alcohol content)
• understand  statistics, charts and tables related to health and wellness studies
• apply the mathematics learned in this course to a number of problems relevant to the sports science educators including:
• scheduling tournaments
• calculations of calories burned, percentage body-fat
• performance monitoring

course prerequisites

Principles of Math 11 C- (or an approved equivalent) or Applications of Math 11 C or DVST 0410 C

curriculum guidelines

Course Guidelines for previous years are viewable by selecting the version desired. If you took this course and do not see a listing for the starting semester/year of the course, consider the previous version as the applicable version.

course schedule and availability
course transferability

Below shows how this course and its credits transfer within the BC transfer system.

A course is considered university-transferable (UT) if it transfers to at least one of the five research universities in British Columbia: University of British Columbia; University of British Columbia-Okanagan; Simon Fraser University; University of Victoria; and the University of Northern British Columbia.

For more information on transfer visit the BC Transfer Guide and BCCAT websites.

assessments