Quantitative Reasoning | |||
QUANT REASON | |||
CLASS CODE: | MATH 108 | CREDITS: 3 | |
DIVISION: | PHYSICAL SCIENCE & ENGINEERING | ||
DEPARTMENT: | MATHEMATICS | ||
GENERAL EDUCATION: | This course fulfills a General Education - Math requirement. | ||
CATALOG DESCRIPTION: | Exploration of contemporary mathematical reasoning covering topics such as logic, problem solving, finance math, linear and exponential modeling, probability and statistics. Will satisfy both the BYU-Idaho and Idaho Core math requirements. Will not serve as a prerequisite for college algebra, trigonometry or any calculus-based courses. | ||
DESCRIPTION: | A course designed to meet the mathematical needs of the liberal arts student. Topics may include mathematical modeling, regression, finance mathematics, probability, statistics, logic, and mathematical patterns and aesthetics. This course will satisfy both the Ricks College and Idaho Core mathematics requirements but will not serve as a prerequisite to other mathematics courses. | ||
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OBJECTIVES: | Upon successful completion of Math 108, a student will be able to meet the following objectives placed in the four core curricular units: UNIT I LOGIC AND PROBLEM SOLVING 1. Recognize and intelligently discuss fallacious reasoning that occurs in various segments of our society. 2. Identify propositions and their corresponding negations, converses, inverses and contrapositives and know what constitutes an argument as well as the differences between deductive and inductive arguments. 3. Explain the difference between valid and invalid arguments, sound and not sound arguments and assess validity and soundness of arguments by using Venn diagrams. 4. Know how to appropriately use George Polya's four-step problem solving guidelines in a meaningful context. UNIT II QUANTITATIVE INFORMATION IN EVERYDAY LIFE 1. View percentages in terms of fractions, changes, comparisons and apply the of versus more than rule. 2. Understand differences between simple and compound interest, APR and APY, discrete and continuous compounds, lump-sum investments, annuities and installment payments. 3. Apply all of the financial formulas to realistic problems involving investments, debt and retirement planning as well as discuss key elements in wise investing (risk, return, liquidity, stocks, bonds, cash, portfolio diversification). 4. Be able to carefully explain the mathematics and dangers of consumer credit and how to appropriately plan. 5. Understand the basics of income tax planning (tax credit vs. deduction, taxable vs. adjusted gross income, standard vs. itemized deductions, marriage penalty, self-employment tax, capital gains taxes). UNIT III PROBABILITY AND STATISTICS 1. Understand differences between descriptive and inferential statistics and the process of a statistical study and key concepts such as simple random samples, placebos, single versus double-blind experiments, observational studies vs. controlled experiments. 2. Determine the validity of a statistical study using the eight guidelines and describe the use and misuse of graphs. 3. Explain how to calculate and interpret statistics such as mean, median, mode, outliers, range, standard, five-number summaries, z-scores, percentiles and margins of error. 4. Identify normal, positively and negatively skewed distributions and apply the 68-95-99.7 rule when appropriate and discuss statistical significance, 95% confidence, confidence intervals, margin of error, hypothesis testing. 5. Understand basic probability rules, law of averages, gambler's fallacy, expected values, at least once rule. UNIT IV MATHEMATICAL MODELING 1. Describe astonishment of exponential growth, that it is growth by a constant % and cannot continue forever. 2. Know how to recognize the differences between linear and non-linear functions. 3. Estimate doubling times and half-life periods using the rule of 70 and apply exponential modeling. 4. Describe logistic growth, overshoot and collapse theory, carrying capacities and population growth behaviors. 5. Understand idea of a function, modeling, independent and dependent variables, domain and range. 6. Be able to calculate slope, the slope-intercept form of a linear function and solve linear problems. |
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REQUIREMENTS: | Graphing calculator may be required for each student. (See class schedule.) | ||
PREREQUISITES: | Math 101 with a grade of "B" or higher or two years of high school algebra. You must also achieve a satisfactory score on the placement exam. The placement exam will cover topics from high school algebra I and II and will be offered during the first week of class. A practice exam is available on the web. | ||
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EFFECTIVE DATE: | August 1999 |