# Topics in Contemporary Mathematics ( MATH 110 A)

## Lecture Note at Union College

Instructor:   Dr. Seongchun (Michelle) Kwon
e-mail:   kwonseon at hotmail dot com

Most video lectures are taken from either ProfRobBob(R) or mathispower4u(J).
I thank to Mr.Tarrou and Prof. Sousa for their willingness to share their high quality lectures for this course.

 PowerPoint ( Partly based on the Powerpoint provided by Cengage Learning ) Video Resource 2. Sets 2.1.Sets: A Problem Solving Tool Introduction to Set Theory (J) Set-Builder Notation (J) Introduction to Subsets(J) 2.2. Set Operations Sets: Union and Intersection (taken from patrickJMT) Please read the powerpoint for difference of sets, disjoint sets and complement of a set 2.3. Venn Diagrams Set Operations and Venn Diagrams: Part 1(J) Set Operations and Venn Diagrams: Part 2(J) 2.4. The Number of Elements in a Set: A Problem Solving Tool Solving Problems with Venn Diagrams (J) 10. Counting Techniques 10.1. The Sequential Counting Principle (SCP): A Problem-Solving Tool The Counting Principle (J) 10.2. Permutations Permutations (J) 10.3. Combinations Combinations (J) 10.4. Miscellaneous Counting Methods Counting Problems (J) 11. Probability 11.1. Sample Spaces and Probability Introduction to Probability (ProfessorSerna) 11.2. Counting Techniques and Probability Intro to Probabilities in Statistics (Full Length) (R): This video clip covers from 11. 1 to 11.3. 11.3. Computation of Probabilities 11.4. Conditional Probability 11.5. Independent Events 11.6. Odds and Mathematical Expectation 12. Statistics 12.1. Sampling, Frequency Distributions, and Graphs Histograms in Statistics (R) Introduction to Histograms (J) 12.2. Measures of Central Tendency: The Mean, Median, and Mode Mean, Median and Mode (J) Ex: Find the Mode of a Data Set (J) Ex: Find the Mean of a Data Set (J) Ex: Find the Median of a Data Set (J) 12.3. Measures of Dispersion: The Range and Standard Deviation Measuring Variation: Range and Standard Deviation(J) 12.4. The Normal Distribution: A Problem and Standard Deviation Introduction to the Normal Distribution(J) Normal Distribution: Z-Scores (J) Normal Distribution: Find Probability Using With Z-scores Using Tables(J) Normal Distribution: Find Probability of Data Values Using Tables (J) 12.5. Statistical Graphs: A Problem Solving Tool Describing Categorical Data Using a Bar Graph, Pareto Chart, Pie Chart, and Pictogram(J) 12.6. Making Predictions: Linear Regression Introduction to Regression Analysis(J) Linear Regression - Least Squares Criterion Part 1( PatrickJMT ) Linear Regression - Least Squares Criterion Part 2( PatrickJMT ): Slope and y-intercept formula here look different. However, those are equivalent formula stated in our textbook. 12.7. Scattergrams and Correlation 13.Your Money and Your Math 13.1. Interest, Taxes, and Discounts The Simple Interest Formula (J) Ex: Determine an Account Balance Using Simple Interest (J) Compounded Interest (J) Ex 1: Compounded Interest Formula - Quarterly (J) Ex:Compounded Interest Formula - Determine Deposit Needed (Present Value) (J) 13.2. Credit Cards and Consumer Credit 13.3. Annual Percentage Rate(APR) and the Rule of 78 13.4. Buying a House 13.5. Investing in Stocks, Bonds, and Mutual Funds