This week we will examine the concept of a function, a fundamental …
This week we will examine the concept of a function, a fundamental concept underlying all of modern mathematics. You’re undoubtedly already familiar with functions in an intuitive sense: a function is something which, given an input, produces an output. But you’ve probably never seen the formal definition of a function as it relates to set theory, which is what we’ll look at this week.
This resource contains a student activity handout, a facilitation guide, example solutions, …
This resource contains a student activity handout, a facilitation guide, example solutions, and class notes. Students work together to discover one-to-one correspondences between various infinite sets of numbers and the set of natural numbers. At the end of this activity the compiled results of their group work form a list of infinite sets that all have the same cardinality as the set of natural numbers. Instructors may take this lesson further by discussion countably infinite versus uncountably infinite sets. This activity aligns with MATH 1332 Learning Outcome 1: Apply the language and notation of sets.
This book will initiate you into an esoteric world. You will learn …
This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.
This course is an introduction to contemporary calculus and is the first …
This course is an introduction to contemporary calculus and is the first of a three-part sequence. In this course students explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl
CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a …
CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.
We told you about the derivatives of many functions, but you might …
We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!
The goal of this class is to prove that category theory is …
The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.
This is a focused collection of notes for a course in college …
This is a focused collection of notes for a course in college algebra taught at San Jacinto College (Houston, Texas). With only 157 pages, this course covers only the core concepts that every college algebra student should know. In addition to learning algebraic and computational skills, the course is designed for learning how to think mathematically. The chapters on mathematical language and problem-solving highlight this latter objective.
This is a focused collection of notes for a course in college …
This is a focused collection of notes for a course in college algebra taught at San Jacinto College (Houston, Texas). With only 157 pages, this course covers only the core concepts that every college algebra student should know. In addition to learning algebraic and computational skills, the course is designed for learning how to think mathematically. The chapters on mathematical language and problem-solving highlight this latter objective.
his book is an introduction to combinatorial mathematics, also known as combinatorics. …
his book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.
This resource contains class notes, an activity handout, and a facilitation guide. …
This resource contains class notes, an activity handout, and a facilitation guide. Students play the game “Let’s Make a Deal” to explore the underlying probability that guides the optimal strategy for contestants. This activity aligns with MATH 1342 Learning Outcome 3: Compute and interpret empirical and theoretical probabilities using the rules of probabilities and combinatorics.
This resource contains a facilitation guide, class notes, and an activity handout. Students …
This resource contains a facilitation guide, class notes, and an activity handout. Students play the game “Let’s Make a Deal” to explore the underlying probability that guides the optimal strategy for contestants. This activity aligns with MATH 1332 Learning Outcome 4: Demonstrate fundamental probability/counting techniques and apply those techniques to solve problems.
This resource contains a slide deck and a facilitation guide. Students are …
This resource contains a slide deck and a facilitation guide. Students are guided to consider how mathematics can help us understand the phenomenon of a pandemic and inform our responses. Students work in groups using the NCTM’s browser pandemic app to manipulate four factors that influence the spread of a virus to see the how changing these variables creates different outcomes. They learn and explore how a log curve is used in this model. This activity aligns with MATH 1332 Learning Outcome 6: Demonstrate the ability to choose and analyze mathematical models to solve problems from real-world settings, including, but not limited to, personal finance, health literacy, and civic engagement
This resource contains a student activity handout, class notes, and a facilitation …
This resource contains a student activity handout, class notes, and a facilitation guide. Students work together to discover one-to-one correspondences between various infinite sets of numbers and the set of natural numbers. At the end of this activity the compiled results of their group work form a list of infinite sets that all have the same cardinality as the set of natural numbers. Instructors may take this lesson further by discussion countably infinite versus uncountably infinite sets. This activity aligns with MATH 1332 Learning Outcome 1: Apply the language and notation of sets
This resource contains a news article about using algorithms to stop gerrymandering …
This resource contains a news article about using algorithms to stop gerrymandering and a lesson plan to pair with the article.Students make predictions, calculator confidence intervals, and discover the Law of Large Numbers via simulation. This lesson can be closed with a discussion of the Central Limit Theorem. This activity aligns with MATH 1342 Learning Outcome 5: Examine, analyze, and compare various sampling distributions for both discrete and continuous random variables and Learning Outcome 6: Describe and compute confidence intervals.
This resource contains a news article and a facilitation guide. Students play …
This resource contains a news article and a facilitation guide. Students play the game “Let’s Make a Deal” to explore the underlying probability that guides the optimal strategy for contestants. This activity aligns with MATH 1342 Learning Outcome 4: Explain the role of probability in statistics.
This resource contains a news article, probability table, statistical study skill, and …
This resource contains a news article, probability table, statistical study skill, and facilitation guide. Students investigate the role of statistics and mathematical modeling in football analysis. This activity aligns with MATH 1342 Learning Outcome 1: Explain the use of data collection and statistics as tools to reach reasonable conclusions.
This site teaches Building Functions to High Schoolers through a series of …
This site teaches Building Functions to High Schoolers through a series of 1355 questions and interactive activities aligned to 13 Common Core mathematics skills.
This site teaches Interpreting Functions to High Schoolers through a series of …
This site teaches Interpreting Functions to High Schoolers through a series of 3578 questions and interactive activities aligned to 38 Common Core mathematics skills.
This site teaches Linear, Quadratic, and Exponential Models to High Schoolers through …
This site teaches Linear, Quadratic, and Exponential Models to High Schoolers through a series of 137 questions and interactive activities aligned to 6 Common Core mathematics skills.
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