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#2: Functions and Relations
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CC BY-NC
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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.

Subject:
Functions
Material Type:
Reading
Author:
Brent Yorgey
Date Added:
06/03/2021
Book of Proof
Only Sharing Permitted
CC BY-ND
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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.

Subject:
Functions
Material Type:
Textbook
Provider:
Virginia Commonwealth University
Author:
Richard Hammack
Date Added:
01/01/2009
Calculus I (MATH 151)
Unrestricted Use
CC BY
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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

Subject:
Calculus
Functions
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Lesson Plan
Reading
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
Date Added:
10/31/2011
Calculus - TI Activities (Teacher's Edition)
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CC BY-NC-SA
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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.

Subject:
Calculus
Functions
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
Date Added:
12/17/2010
Category Theory for Scientists, Spring 2013
Conditional Remix & Share Permitted
CC BY-NC-SA
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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.

Subject:
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
David I. Spivak
Date Added:
01/01/2013
Combinatorics Through Guided Discovery
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Some Rights Reserved
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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.

Subject:
Mathematics
Functions
Material Type:
Textbook
Provider:
Dartmouth College
Author:
Kenneth Bogart
Date Added:
01/01/2004
Functions: Interpreting Functions
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CC BY-NC-SA
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This site teaches Interpreting Functions to High Schoolers through a series of 3578 questions and interactive activities aligned to 38 Common Core mathematics skills.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Functions: Linear, Quadratic, and Exponential Models
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CC BY-NC-SA
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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.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Functions: Trigonometric Functions
Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Trigonometric Functions to High Schoolers through a series of 915 questions and interactive activities aligned to 15 Common Core mathematics skills.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
08/13/2020
Introduction To MATLAB Programming, Fall 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
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This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB in particular.

Subject:
Computer Science
Information Science
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Yossi Farjoun
Date Added:
01/01/2011
Introduction to C++, January IAP 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

This is a fast-paced introductory course to the C++ programming language. It is intended for those with little programming background, though prior programming experience will make it easier, and those with previous experience will still learn C++-specific constructs and concepts. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subject:
Computer Science
Information Science
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dunietz, Jesse
Kovacs, Geza
Marrero, John
Date Added:
01/01/2010
Introduction to Functional Analysis, Spring 2009
Conditional Remix & Share Permitted
CC BY-NC-SA
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" This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem."

Subject:
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Melrose, Richard
Date Added:
01/01/2009
Introduction to Real Analysis
Conditional Remix & Share Permitted
CC BY-NC-SA
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This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.

Subject:
Mathematics
Calculus
Functions
Material Type:
Textbook
Provider:
Trinity University
Provider Set:
Digital Commons @Trinity University
Author:
William Trench
Date Added:
12/01/2013
Modeling Dynamics and Control I, Spring 2005
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CC BY-NC-SA
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First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

Subject:
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dubowsky, Steven
Trumper, David L.
Date Added:
01/01/2005
OpenStax College Algebra TestGen Testbank for Chapters 1 & 2
Unrestricted Use
CC BY
Rating
5.0 stars

The attached file is a .bok TestGen file which contains the first two chapters of the OpenStax College Algebra Textbook. Using the TestGen software, one can create quizzes, tests and homework assignments compatible with Canvas, Blackboard, Moodle and D2L.

Subject:
Algebra
Functions
Numbers and Operations
Ratios and Proportions
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Textbook
Unit of Study
Author:
Larry Whittington
Date Added:
12/20/2021
Precalculus I (MATH 141)
Unrestricted Use
CC BY
Rating
0.0 stars

This course will cover families of functions, their properties, graphs and applications. These functions include: polynomial, rational, exponential, logarithmic functions and combinations of these. We will solve related equations and inequalities and conduct data analysis, introductory mathematical modeling and develop competency with a graphing calculator.Login: guest_oclPassword: ocl

Subject:
Functions
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Lesson Plan
Reading
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
Date Added:
10/31/2011
Sample MATH 2412 PreCalculus OpenStax Syllabus
Unrestricted Use
CC BY
Rating
5.0 stars

This is an example of a redesigned course that uses the OpenStax PreCaculus Textbook. Emphasis is placed on the structure of course (which is not conics centric) and how homework is implemented. To avoid the financial responsiblity of the student or higher education institution purchasing publisher online homework services like Pearson's MyMathLab, ConnectMath or Aleks; students are assigned exercises from the textbook that have answers available. The strategy is to give access to the answers of the problems so that the students have to prove how the answer was obtained. This allows the students some immediate feedback if their written process does not obtain the solution given in the back of the textbook.This allows the student to recognize that a process, operation or strategy was carried out incorrectly which can be used to draw attention that a question needs to be raised during the next lecture or additional assistance may be required on their journey to mastery of the content.

Subject:
Mathematics
Algebra
Calculus
Functions
Ratios and Proportions
Material Type:
Full Course
Homework/Assignment
Syllabus
Author:
Larry Whittington
Date Added:
12/23/2021
Spiral Workbook for Discrete Mathematics
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CC BY-NC-SA
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This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

Subject:
Mathematics
Functions
Numbers and Operations
Material Type:
Textbook
Provider:
State University of New York
Provider Set:
Milne Open Textbooks
Author:
Harris Kwong, SUNY Fredonia
Date Added:
11/06/2015