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.

# 761 Results

APEX Calculus is a calculus textbook written for traditional college/university calculus courses. It has the look and feel of the calculus book you likely use right now (Stewart, Thomas & Finney, etc.). The explanations of new concepts is clear, written for someone who does not yet know calculus. Each section ends with an exercise set with ample problems to practice & test skills (odd answers are in the back).

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- APEX: Affordable Print and Electronic TeXtbooks
- Author:
- Brian Heinold
- Dimplekumar Chalishajar
- Gregory Hartman
- Troy Siemers
- Date Added:
- 01/01/2014

This text was written as a prequel to the APEXCalculus series, a three–volume series on Calculus. This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses. The topics were chosen based on experience; several instructors in the Applied Mathemathics Department at the Virginia Military Institute (VMI) compiled a list of topics that Calculus students commonly struggle with, giving the focus of this text. This allows for a more focused approach; at first glance one of the obvious differences from a standard Pre-Calculus text is its size.

This is a quick guide to help students differenciate the terms APR and APY. There are formulas presented to help students calculate APY given certain parameters of investments. The guide also presents formulas to allow students to calculate APY outside of the traditional one year examples.

- Subject:
- Mathematics
- Material Type:
- Student Guide
- Author:
- George Swindell
- Date Added:
- 07/29/2021

This book is designed to make "Abstract Algebra" as down-to-earth as possible. Using concrete examples such as the complex numbers, integers mod n, polynomials, symmetries, and permutations. We also introduce some of the beautifully general ideas of the theory of groups, rings, and fields. Along the way, we give applications to signal processing, cryptography and coding theory, as well as making connections with other branches of mathematics such as geometry and number theory.

The textbook is provided in three different formats: hyperlinked online version, pdf, and spiral bound copy (printme1.com is recommended for on-demand printing).

- Subject:
- Algebra
- Material Type:
- Homework/Assignment
- Textbook
- Author:
- Christopher Thron
- Justin Hill
- Date Added:
- 06/15/2021

This text is intended for a one- or two-semester undergraduate course in abstract algebra. Traditionally, these courses have covered the theoretical aspects of groups, rings, and fields. However, with the development of computing in the last several decades, applications that involve abstract algebra and discrete mathematics have become increasingly important, and many science, engineering, and computer science students are now electing to minor in mathematics. Though theory still occupies a central role in the subject of abstract algebra and no student should go through such a course without a good notion of what a proof is, the importance of applications such as coding theory and cryptography has grown significantly.

- Subject:
- Algebra
- Material Type:
- Textbook
- Provider:
- University of Puget Sound
- Author:
- Thomas Judson
- Date Added:
- 01/01/2016

Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

- Subject:
- Mathematics
- Calculus
- Material Type:
- Textbook
- Provider:
- Grand Valley State University
- Author:
- David Austin
- Matt Boelkins
- Steve Schlicker
- Date Added:
- 08/13/2020

Active Calculus Multivariable is the continuation of Active Calculus to multivariable functions. The Active Calculus texts are different from most existing calculus texts in at least the following ways: the texts are free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the texts are open source, and interested instructors can gain access to the original source files upon request; the style of the texts requires students to be active learners — there are very few worked examples in the texts, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number and challenging in nature.

- Subject:
- Calculus
- Material Type:
- Textbook
- Provider:
- Grand Valley State University
- Author:
- David Austin
- Matthew Boelkins
- Steven Schlicker
- Date Added:
- 07/01/2018

To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.

- Subject:
- Algebra
- Material Type:
- Lesson
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 08/13/2020

This is book one in a six-book series on fundamental mathematics for adult learners. These books include glossaries, self tests, practice requests, grades records, and unit tests. Ancillary Resources include the Instructor's Manual. Topics in this book include: number and number operations, patterns, functions and relations, real life applications, geometry, and time.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Provider:
- BCcampus
- Author:
- Liz Girard
- Wendy Tagami
- Date Added:
- 07/22/2021

This textbook is part of the OpenIntro Statistics series and offers complete coverage of the high school AP Statistics curriculum. Real data and plenty of inline examples and exercises make this an engaging and readable book. Links to lecture slides, video overviews, calculator tutorials, and video solutions to selected end of chapter exercises make this an ideal choice for any high school or Community College teacher. In fact, Portland Community College recently adopted this textbook for its Introductory Statistics course, and it estimates that this will save their students $250,000 per year. Find out more at: openintro.org/ahss

View our video tutorials here:

openintro.org/casio

openintro.org/TI

- Subject:
- Statistics and Probability
- Material Type:
- Textbook
- Provider:
- OpenIntro
- Author:
- Christopher Barr
- David Diez
- Leah Dorazio
- Mine Cetinkaya-Rundel
- Date Added:
- 08/13/2020

" The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc."

- Subject:
- Algebra
- Material Type:
- Full Course
- Provider:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Rosales, Rodolfo R.
- Date Added:
- 01/01/2009

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Provider:
- Open Book Publishers
- Author:
- Stephen Siklos
- Date Added:
- 08/13/2020

Learning and Understanding Mathematical Concepts in the Areas of Water Distribution and Water Treatment

- Subject:
- Mathematics
- Hydrology
- Material Type:
- Textbook
- Provider:
- College of the Canyons
- Author:
- Michael Alvord
- Regina Blasberg
- Date Added:
- 08/13/2020

These courses, produced by the Massachusetts Institute of Technology, introduce the fundamental concepts and approaches of aerospace engineering, highlighted through lectures on aeronautics, astronautics, and design. MIT˘ďď_s Aerospace and Aeronautics curriculum is divided into three parts: Aerospace information engineering, Aerospace systems engineering, and Aerospace vehicles engineering. Visitors to this site will find undergraduate and graduate courses to fit all three of these areas, from Exploring Sea, Space, & Earth: Fundamentals of Engineering Design to Bio-Inspired Structures

- Subject:
- Engineering
- Mathematics
- Chemistry
- Physics
- Material Type:
- Full Course
- Provider:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Date Added:
- 03/17/2011

This book is a guide to implement simple agent-based evolutionary models using NetLogo.

- Subject:
- Mathematics
- Material Type:
- Textbook
- Author:
- Luis R. Izquierdo
- Segismundo S. Izquierdo
- William H. Sandholm
- Date Added:
- 08/13/2020

Algebra 1 Course Outline

This site teaches Arithmetic with Polynomials and Rational Expressions to High Schoolers through a series of 4333 questions and interactive activities aligned to 26 Common Core mathematics skills.

- Subject:
- Mathematics
- Algebra
- Material Type:
- Activity/Lab
- Interactive
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 08/13/2020

This site teaches High Schoolers how to create equations through a series of 298 questions and interactive activities aligned to 5 Common Core mathematics skills.

- Subject:
- Mathematics
- Algebra
- Material Type:
- Activity/Lab
- Interactive
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Date Added:
- 08/13/2020

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.

- Subject:
- Algebra
- Material Type:
- Full Course
- Provider:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Artin, Michael
- Date Added:
- 01/01/2011