- Course type: Self-paced
- Available Lessons: 106
- Average Lesson Length: 8 min
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Watch a preview:chapter 1 / lesson 1Critical Thinking and Logic in Mathematics
Course SummaryBoost your understanding of contemporary math topics, such as graph theory, mathematical reasoning, probability and more, with this study course. Use the short video lessons to supplement the subjects you're learning about in class, and then take the quizzes to measure how well you understand and remember these math concepts.
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Course Practice TestCheck your knowledge of this course with a 50-question practice test.
- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
About This Course
This course presents an overview of contemporary math concepts, principles and applications. The math professionals who teach the lessons will guide you through lessons on solving math word problems, developing discrete probability distributions and understanding the mathematics of voting and apportionment. You'll learn about graph theory, probability concepts and statistical measures through quick and comprehensive video lessons. When you've finished all the lessons in this course, you'll be familiar with:
- Mathematical reasoning and logic
- Different types of samples
- Probability of independent and dependent events
- Continuous probability distributions
- Apportionment methods
- Election math methods
|Mathematical Reasoning & Problem-Solving||Determine how logic and critical thinking are used in math and explain logical fallacies, truth values and conditional statements. Examine math principles for problem solving and different types of reasoning.|
|Solving Math Word Problems||Describe the steps used to solve word problems and apply them to multi-step word problems. Explain how to restate word problems with words or images and use personal situations to make the problem more understandable.|
|Statistics Overview||Differentiate between descriptive and inferential statistics and populations and samples. Examine the different types of random samples and learn to calculate mean, find percentiles in a data set, calculate percent increases and create histograms.|
|Probability Overview||Explain math set theory and identify subsets. Learn to find the probability of simple events, calculate conditional probabilities and evaluate independence. Discuss math combinations and permutations.|
|Discrete Probability Distributions||Find expected values of discrete random variables and games of chance. Learn to use formulas and tables to find binomial probabilities and solve problems with binomial experiments.|
|The Normal Curve & Continuous Probability Distributions||Graph probability distributions and interpret the expected value of a continuous random variable. Explain how to develop continuous probability distributions. Describe how to use normal distribution and z-scores.|
|The Mathematics of Voting||Define preference ballots and schedules and explain the plurality method of elections in math. Learn how the borda count method and plurality with elimination methods work. Demonstrate candidate ranking methods and discuss Arrow's Impossibility Theorem.|
|The Mathematics of Apportionment||Describe the problem of apportionment in political representation and list the steps in Hamilton's Method of Apportionment. Examine the Quota Rule, population paradoxes and Jefferson, Adams and Webster's apportionment methods.|
|Graph Theory||Describe Euler Paths and Euler's Circuits. Understand Fleury's algorithm, Hamilton Circuits and Hamilton Paths. Define a weighted graph and explain methods for finding the most efficient circuit|
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