This task is intended strictly for instructional purposes with the goal of building understandings of linear relationships within a meaningful and, hopefully, somewhat familiar context.

This course covers relations and functions, specifically, linear, polynomial, exponential, logarithmic, and rational functions. Additionally, sections on conics, systems of equations and matrices and sequences are also available.

This College Algebra textbook provides a comprehensive introduction to the fundamental concepts of algebra, with a unique focus on the concept of inverses. The textbook begins with an exploration of the foundational principles of functions, including domain, range, and the vertical line test. It progresses through critical topics such as operations on functions, composition of functions, and the algebra of functions, ensuring students grasp the fundamental building blocks necessary for more complex algebraic thinking.Several times the teaching diverges from how the subject is commonly taught. Examples include absolute value, determining the inverse of a function, and completing the square. The text is as devoid of "gimmicks" or "tricks" as possible, leaning on the fundamentals of good algebra. Also, there is a high reliance on fractions, rather than decimal numbers, to help equip the student with the better way to read a problem and its solution.This book is written for and dedicated to my grandchildren, and the fact that you're taking at least a glimpse of it is just a huge bonus! Thank you.

Developed as part of a Round 13 Mini-Grant, these updated supplementary materials for Stitz-Zeager Open Source Mathematics and the LibGuides Open Course for College Algebra at GCSU include notes and exercises on equations, inequalities, functions, polynomial and rational functions, and exponential and logarithmic functions are included in one .zip file.

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 task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations.

This task is preliminary to F-LE Compounding Interest with a 5% Interest Rate which further develops the relationship between e and compound interest.

This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically addresses the standard (F-BF), building functions from a context, a auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.

This textbook, Counting Rocks!, is the written component of an interactive introduction to combinatorics at the undergraduate level. Throughout the text, we link to videos where we describe the material and provide examples; see the Youtube playlist on the Colorado State University (CSU) Mathematics YouTube channel.

The major topics in this text are counting problems (Chapters 1-4), proof techniques (Chapter 5), recurrence relations and generating functions (Chapters 6-7), and graph theory (Chapters 8-12). The material and the problems we include are standard for an undergraduate combinatorics course. In this text, one of our goals was to describe the mathematical structures underlying problems in combinatorics. For example, we separate the description of sequences, permutations, sets and multisets in Chapter 3.

In addition to the videos, we would like to highlight some other features of this book. Most chapters contain an investigation section, where students are led through a series of deeper problems on a topic. In several sections, we show students how to use the free online computing software SAGE in order to solve problems; this is especially useful for the problems on recurrence relations. We have included many helpful figures throughout the text, and we end each chapter (and many of the sections) with a list of exercises of varying difficulty.

This word problem requires students to create expressions to calculate gas milage for a vehicle.

The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context.

In this lesson, students measure and compare the rate of a falling object (a penny) at different heights to learn about statistical error.

In this visualization adapted from the University of Massachusetts Medical School, discover the role that dengue viral proteins play in a human cell as the virus prepares to replicate.

Interactive Desmos activities that are associated with Units of the Secondary Math II - Mathematics Vision Project (MVP) curriculum.
Teachers will want to create a class code to share with students to monitor student progress as they work through the Desmos activities for each of the lessons.

This task asks students to find a linear function that models something in the real world. After finding the equation of the linear relationship between the depth of the water and the distance across the channel, students have to verbalize the meaning of the slope and intercept of the line in the context of this situation.

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).

This task is designed as a follow-up to the task F-LE Do Two Points Always Determine a Linear Function? Linear equations and linear functions are closely related, and there advantages and disadvantages to viewing a given problem through each of these points of view. This task is intended to show the depth of the standard F-LE.2 and its relationship to other important concepts of the middle school and high school curriculum, including ratio, algebra, and geometry.

This problem complements the problem ``Do two points always determine a linear function?''

The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable, and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).