Math 106
COURSE OBJECTIVES
I. Measuring or Counting Quantitative with Units and Using Them in Problem Solving
P.I.1
Determine Common Fractions.
P.I.2
Add and Subtract Fractions
P.I.3
Multiply Fractions
P.I.4
Simplify Reciprocals and Division
P.I.5
Convert from Fraction to Decimal
P.I.6
Convert from Decimal to Fraction (for some rational numbers)
I.7
Identify Different Types of Units
I.8
Use Conversion Factors to Convert Units
I.9
Chose the Most Appropriate Units in the Standardized U.S. Units System for a Measurement
I.10
Chose the Most Appropriate Units in the Standardized Metric Units System for a Measurement
I.11
Convert Units between the U.S. and Metric System
I.12
Convert Units in the Form That Is Raised to Some Powers
I.13
Convert Temperature Units (between Celsius, Fahrenheit, and Kelvin)
I.14
Solve Words Problem That Involve Units Conversion
II. Informal and Formal Logic
P.II. 1
Identify Set of Natural Numbers, Set of Whole Numbers, and Set of Integers
P.II.2
Identify Set of Rational and Irrational Numbers
P.II.3
Use Venn Diagrams to Partition Subset of a Set
P.II.4
Use (Informal) Logic in If…, then… Form
P.II.5
Use (Informal) Logic in …Or … Form
P.II.6
Use (Informal) Logic in …And… Form
II.7
Identify Varies Fallacies: Appeal to Popularity, False Cause, Appeal to Ignorance, Hasty Generalization, Limited Choice,
Appeal to Emotion, Personal Attack, Circular Reasoning, Diversion, Straw Man
II.8
Construct and Apply Truth Table for items in II.P.4-6.
II.9
Evaluate Equivalent Truth Table
II.10
Identify Different Variation on the Conditional: Converse, Inverse, Contrapositive, negation
II.11
Convert Different Variation on the Conditional in English Sentences
II.12
Identify Premise and Conclusion of an Argument, Inductive and Deductive Argument
II.13
Use Venn Diagrams to Solve Problems in Set Theory with And or Or Logic
II.14
Use Venn Diagrams to Test a Conditional Argument’s Validity
II.15
Apply Quantitative Reasoning to Evaluate a Given Situation or Pending Decision
III. Usage of Percentage and Price Index
P.III.1
Apply the Definition of Percentages
P.III.2
Discuss Ratio, Percentage, and Fraction
P.III.3
Convert between Ratio, Percentage and Fraction(and some Decimal)
P.III.4
Multiply and Add number written in the Power of 10
P.III.5
Calculate Value of Certain Percentage, and Able to Use Percentage for Comparison
III.6
Identify the Different between Percentage Points and Percentage
III.7
Compute Absolute and Relative Difference
III.8
Apply Definition of Scientific Notation and Use it for Calculation
III.9
Identify Random Error, Systematic Error, Accuracy and Precision
III.10
Compute Index Number and Inflation
III.11
Apply and Discuss the Consumer Price Index
III.12
Adjust Prices for Inflation
III.13
Identify Simpson’s Paradox
III.14
Evaluate Several Common Misusage of Conditional Probability (versus Probability): Polygraph Test and Mammogram
Test
III.15
Identify Potential Number Deception Based on Different Point of Views of a Data Set: The Republican and Democratic
Views of a Tax Cut
IV. Common Calculation in Money Management
P.IV.1
Identify Real Variables (such as x , y ) in Equations
P.IV.2
P.IV.3
P.IV.4
P.IV.5
IV.6
IV.7
IV.8
IV.9
IV.10
Apply a Given Mathematical Formula
Solve for an Exact Solution of a Linear Equation with One Variable
Evaluate Numerical Expression in Exponential and Root Form
Identify Simple and Compound Interest
Evaluate Simple and Compound Interest ( n Times per Year)
Evaluate Annual Percentage Yield
Evaluate Continuous Compound Interest by Using a Formula
Evaluate Annuity by Using the Saving Plan and Loan Formula
Evaluate Total and Annual Return of an Investment
IV.11
IV.12
IV.13
IV.14
IV.15
IV.16
IV.17
IV.18
IV.19
IV.20
IV.21
IV.22
IV.23
Identify investment types: Stock, Bond, and Cash
Evaluate the Price to Earning Ratio, Earning Per Share of a Stock
Evaluate the Current Yield of a Bond
Discuss the Repayment Strategies in a Loan
Discuss Some Common Practices, Strategies in Using Credit Cards and getting a Mortgage or Loan
Apply the Definition of Deduction, Tax Credits, and Exemption in Federal Income Tax
Calculate Basic Federal Income Taxes
Calculate Social Security and Medicare Taxes
Identify Receipts, Outlays, Net Income, Surplus, Deficit, Debt in a Budget
Discuss of the Current Federal Debt
Discuss of the Current Social Security Problem
Evaluate Publicly Held Debt, Gross Debt, Off-Budget, and In-Budget Net Income of the Federal Budget through Given
Formulas
Discuss the Basic Principles of the Federal Budget: How to Finance its Debts
V. Statistical Reasoning
P.V.1
Discuss Information from Statistical Tables and Graphs: Pie, Bar Graph, and Frequency Table
P.V.2
Discuss Information from Line Graph and Bar Graph in General
P.V.3
Discuss and Construct Graph of Points in a Standard Coordinate Plane (Scatter Diagram)
V.4
Discuss True Randomness, Observed Randomness, and Representative Statistic
V.5
Identify the Population, Sample and Population Parameters of a Statistic
V.6
Identify and Construct Four Types of Sampling Methods: Simple Random, Systematic, Convenience, Stratified
V.7
Distinguish between Two Types of Statistical Study: Observational Study and Experiment
V.8
Identify and Discuss Placebo Effect, Single Blind, and Double Blind Study in Statistic
V.9
Apply Margin of Error by a Given Confidence Interval to Evaluate Result of a Statistic
V.10
Evaluate the Validity of a Statistical Study and Its Claim
V.11
Interpret and Create Stack Graph, Frequency Tables, Bar Graph, Pie Graph, Histogram, and Line Graph
V.12
Interpret Multiple Bar Graphs, Stack Plots, Contour Maps and Other Media Graphs
V.13
Distinguish between Three-Dimensional and Two-Dimensional Data and Their Graphs
V.14
Distinguish between Correlation and Causality
V.15
Identify Positive, Negative, or No Correlation of a Scatter Diagram
V.16
Understand and Apply Six Guidelines for Establishing Causality
VI. Statistic
P.VI.1
Discuss chance and how likely an event could happen
P.VI.2
Rank Real Numbers
P.VI.3
Calculate and Identify Mean, Median and Mode
VI.4
Calculate and Identify Mean, Median, and Mode
VI.5
Identify and Understand the Effects of Outliers
VI.6
Construct and Read Information form a Distribution Graph
VI.7
Identify Several Distribution: Normal, Standard Normal, Symmetric, Uniform, Finite Discrete, and Skew
VI.8
Calculate Range, Standard Deviations
VI.9
Interpret Standard Deviation in General
VI.10
Discuss 68-95-99.7 Rule in a Normal Distribution
VI.11
Discuss Central Limit Theorem and Sampling Distribution of a Mean
VI.12
Discuss the Relationship between Chance and Level of Significance, Confidence Level
VI.13
Use Standard Deviation to find Percentile in a Normal Distribution Using a z-score Table, Vice Versa
VI.14
Estimate the Margin of Error of a Mean at 95% Confidence Level
VI.15
Construct Null and Alternative Hypothesis Testing of the Mean of a One Sample Statistic
VI.16
Discuss the Method of Hypothesis Testing of the Mean of a One Sample Statistic
VII. Probability
P.VII. 1 Apply the Multiplication Principle in Counting
P.VII.2
Discuss Possible Outcome of Some Simple Game: Rolling 6-Faced Dice and Tossing Coin.
P.VII.3
Convert Factorials to Whole Numbers or Fraction
VII.4
Distinguish the Three Types of Probability: Theoretical, Empirical, and Subjective
VII.5
Apply Finite Countable Definition of Theoretical Probabilities to Calculate Probability
VII.6
Construct Probability Distribution Table and/or Graph
VII.7
Identify Independent and Dependent Events
VII.8
Identify Overlapping or Non Overlapping Events
VII.9
Compute Probability with Overlapping, Non Overlapping, Independent, and Dependent Events
VII.10
Compute Probability of the Type “at Least Once in n Trials”
VII.11
Compute and Measure Risk in Terms of Death Rates and Accident
VII.12
Count with Permutations and Combinations
VII.13
Apply Permutation and Combination Formula
VII.14
Discuss Gambler’s Fallacy
VII.15
Calculate Expected Value in a Finite Discrete Probability and its Events.
VIII. Linear and Exponential Growth
VIII.P.1 Identify Linear Growth
VIII.P.2
VIII.P.3
VIII.P.4
VIII.P.5
VIII.6
VIII.7
VIII.8
VIII.9
VIII.10
VIII.11
VIII.12
VIII.13
Identify Exponential Growth
Translate between Logarithm Equation and Exponential Equation
Compute Numerical Value with Logarithm Equation in Base 10
Compute Numerical Value Using the Addition and/or Multiplication Rules for Logarithms
Distinguish Linear and Exponential Growth
Discuss Doubling Time and Half Life time
Apply Formula to Approximate Doubling Time and Half Life
Apply Formula to Compute Doubling Time and Half Life
Discuss the Definition of Logistic Growth Rate
Discuss the Effect of Overshoot and Collapse and Its Relationship with Exponential Growth
Discuss Carrying Capacity
Apply Mathematical Formula to Compute Earthquake Magnitude Scale, Decibel Scale, and pH Scale
IX. Mathematical Model
IX.P.1
Discuss the Definition of a Real Value Function of One Variable
IX.P.2
Identify Dependent Variable and Independent Variable of a Function
IX.P.3
Represent Ordered Pairs in a Function When Appropriate
IX.P.4
Identify the Domain and Range of a Function
IX.P.5
Graph Linear Equation if Their Equation is Provided in Slope Intercept Form ( y = mx + b )
IX.P.6
Write Linear Equation in Standard Form if Their Graph is Provided
IX.P.6
Discuss and Compute Slopes, Rate of Change by Two Provided Coordinates or a Equation
IX.P.7
Find Equation of a Line by Two Provided Coordinates
IX.P.8
Solve Exponential Equation of the Type a x = b Using Logarithms of Based 10
IX.9
IX.10
IX.11
IX.12
IX.13
IX.14
Discuss the Notation f (x ) as a Function
Represent One Variable Real Functions with a Data Table, Graph, or Equation.
Translate between the Concept of Rate of Change, Slope, and m in Linear Equation in Slope Intercept Form
Identify and Construct Linear Model in Word Problems
Identify and Construct Exponential Model in Word Problems
Apply Formula to Compute Half Life and Doubling Time Related Problems (VIII.8 and VIII.9)