Mathematics Textbooks and Full Courses

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Mathematics Textbooks and Full Courses Collection Resources (300)

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Abstract Algebra II
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This course is a continuation of Abstract Algebra I: the student will revisit structures like groups, rings, and fields as well as mappings like homomorphisms and isomorphisms. The student will also take a look at ring factorization, general lattices, and vector spaces. Later this course presents more advanced topics, such as Galois theory - one of the most important theories in algebra, but one that requires a thorough understanding of much of the content we will study beforehand. Upon successful completion of this course, students will be able to: Compute the sizes of finite groups when certain properties are known about those groups; Identify and manipulate solvable and nilpotent groups; Determine whether a polynomial ring is divisible or not and divide the polynomial (if it is divisible); Determine the basis of a vector space, change bases, and manipulate linear transformations; Define and use the Fundamental Theorem of Invertible Matrices; Use Galois theory to find general solutions of a polynomial over a field. (Mathematics 232)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Advanced Algebra II: Activities and Homework
Conditions of Use:
No Strings Attached
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This is the main text of Kenny Felder's course in Advanced Algebra II. It consists of a series of worksheets, some intended to be used in class as group activities, and some intended to be used as homework assignments. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Teacher's Guide" collections to make up the entire course.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Provider:
Rice University
Provider Set:
Connexions
Author:
Kenny Felder
Advanced Algebra II: Teacher's Guide
Conditions of Use:
No Strings Attached
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This is the Teacher's Guide for Kenny Felder's course in Advanced Algebra II. This guide is *not* an answer key for the homework problems: rather, it is a day-by-day guide to help the teacher understand how the author envisions the materials being used. This text is designed for use with the "Advanced Algebra II: Conceptual Explanations" and the "Advanced Algebra II: Homework and Activities" collections (coming soon) to make up the entire course.

Subject:
Algebra
Material Type:
Full Course
Teaching/Learning Strategy
Provider:
Rice University
Provider Set:
Connexions
Author:
Kenny Felder
Advanced Partial Differential Equations with Applications, Fall 2009
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" 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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Rosales, Rodolfo R.
Advanced Statistics
Conditions of Use:
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This course is oriented toward US high school students. The course is divided into 10 units of study. The first five units build the foundation of concepts, vocabulary, knowledge, and skills for success in the remainder of the course. In the final five units, we will take the plunge into the domain of inferential statistics, where we make statistical decisions based on the data that we have collected.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
The Saylor Foundation
Algebra
Conditions of Use:
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This course discusses how to use algebra for a variety of everyday tasks, such as calculate change without specifying how much money is to be spent on a purchase, analyzing relationships by graphing, and describing real-world situations in business, accounting, and science.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Algebra
Conditions of Use:
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The branch of mathematics that treats the relations and properties of quantity by means of letter and other symbols. It is applicable to those relations that are true of every kind of magnitude. Source: Websters Dictionary.

Subject:
Engineering
Algebra
Material Type:
Full Course
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
K-12 Outreach,
TeachEngineering.org
Algebra 1 (A)
Conditions of Use:
No Strings Attached
Rating

The main goal of Algebra is to develop fluency in working with linear equations. In this course, students will work with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will learn how to simplify polynomials and begin to study quadratic relationships, along with analyzing mathematical situations verbally, numerically, graphically, and symbolically. Throughout the course, students will have opportunities to apply mathematical skills and make meaningful connections to lifeŐs experiences.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lesson Plan
Provider:
Mountain Heights Academy
Author:
Individual Authors
Algebra 1 (B)
Conditions of Use:
No Strings Attached
Rating

The main goal of Algebra is to develop fluency in working with linear equations. In this course, students will work with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Students will learn how to simplify polynomials and begin to study quadratic relationships, along with analyzing mathematical situations verbally, numerically, graphically, and symbolically. Throughout the course, students will have opportunities to apply mathematical skills and make meaningful connections to lifeŐs experiences.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lesson Plan
Provider:
Mountain Heights Academy
Author:
Individual Authors
Algebra 2 (A)
Conditions of Use:
No Strings Attached
Rating

Algebra 2 builds upon and extends concepts from both Algebra 1 and Geometry. In Algebra 2, students work with equations, inequalities, and graphs of linear, quadratic, trigonometric, rational, radical, exponential, and logarithmic functions. Real-world applications that can be modeled by each of these functions are explored. Algebra 2 also introduces students to concepts of probability and statistics.

Subject:
Algebra
Statistics and Probability
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lesson Plan
Provider:
Mountain Heights Academy
Author:
Individual Authors
Algebra 2 (B)
Conditions of Use:
No Strings Attached
Rating

Algebra 2 builds upon and extends concepts from both Algebra 1 and Geometry. In Algebra 2, students work with equations, inequalities, and graphs of linear, quadratic, trigonometric, rational, radical, exponential, and logarithmic functions. Real-world applications that can be modeled by each of these functions are explored. Algebra 2 also introduces students to concepts of probability and statistics.

Subject:
Algebra
Statistics and Probability
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lesson Plan
Provider:
Mountain Heights Academy
Author:
Individual Authors
Algebra2Go - Prealgebra
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Prepare yourself to take an Algebra course with the Algebra2go䋢 prealgebra resources page. Whether you are attending Saddleback College's prealgebra class (math 351), taking a prealgebra class at another school, or need to refresh your math skills for a business or science class, Professor Perez and his favorite student Charlie have the tools that can help you. We have five primary types of study materials: class notes, video worksheets, video lectures, practice problems, and practice quizzes. For some topics we have some additional tools to assist you.

Subject:
Algebra
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra2go:  Decimals
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Part of the course for community college students featuring Professor Perez and his student Charlie, teaching about decimal concepts and operations.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lecture
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra2go- PreAlgebra - Intro to Subtraction
Conditions of Use:
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This course is for community college students featuring Professor Perez and his student Charlie. This lesson demonstrates subtraction, including when the answer is negative, on the number line.

Subject:
Algebra
Material Type:
Assessment
Full Course
Lecture
Lecture Notes
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra2go: Pre-algebra Conversions
Conditions of Use:
No Strings Attached
Rating

This is part of the course for community college students featuring Professor Perez and his student Charlie, teaching how to make conversions between different kinds of units.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Lecture
Unit of Study
Provider:
Saddleback College
Provider Set:
Individual Authors
Author:
Candice Harrington
Larry Perez
Patrick Quigley
Algebra A (A)
Conditions of Use:
No Strings Attached
Rating

Algebra A (A) is the first semester of Algebra A.ĘAlgebra A and Algebra B make up a two-year Algebra program. The main goal of Algebra is to develop fluency in working with linear equations. This 2 year program gives students the opportunity to study, learn, and practice algebraic concepts at a pace that allows additional learning activities, projects, and discussions. In this course, students will work with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Throughout the course, students will have opportunities to apply mathematical skills and make meaningful connections to lifeŐs experiences.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lesson Plan
Provider:
Mountain Heights Academy
Author:
Individual Authors
Algebra B (A)
Conditions of Use:
No Strings Attached
Rating

Algebra B (A) is the first semester of Algebra B.Algebra A and Algebra B make up a two-year Algebra program. The main goal of Algebra is to develop fluency in working with linear equations. This 2 year program gives students the opportunity to study, learn, and practice algebraic concepts at a pace that allows additional learning activities, projects, and discussions. In this course, students will work with tables, graphs, and equations and solve linear equations and inequalities and systems of linear equations and inequalities. Throughout the course, students will have opportunities to apply mathematical skills and make meaningful connections to lifeŐs experiences.

Subject:
Algebra
Material Type:
Activity/Lab
Full Course
Homework/Assignment
Lesson Plan
Provider:
Mountain Heights Academy
Author:
Individual Authors
Algebra I
Conditions of Use:
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This course is oriented toward US high school students. Its structure and materials are aligned to the US Common Core Standards. Foci include: graphing, equations and inequalities.

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation
Algebra II, Spring 2011
Conditions of Use:
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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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Artin, Michael
Algebraic Combinatorics, Spring 2009
Conditions of Use:
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" This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but assumes a familiarity with linear algebra and finite groups. Topics were chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected."

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Musiker, Gregg
Algebraic Geometry, Spring 2009
Conditions of Use:
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" This course provides an introduction to the language of schemes, properties of morphisms, and sheaf cohomology. Together with 18.725 Algebraic Geometry, students gain an understanding of the basic notions and techniques of modern algebraic geometry."

Subject:
Algebra
Geometry
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Kedlaya, Kiran
Algebraic Techniques and Semidefinite Optimization, Spring 2006
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This research-oriented course will focus on algebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization. The course will develop in a parallel fashion several algebraic and numerical approaches to polynomial systems, with a view towards methods that simultaneously incorporate both elements. We will study both the complex and real cases, developing techniques of general applicability, and stressing convexity-based ideas, complexity results, and efficient implementations. Although we will use examples from several engineering areas, particular emphasis will be given to those arising from systems and control applications.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Parrilo, Pablo
Algebraic Topology II, Spring 2006
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In this second term of Algebraic Topology, the topics covered include fibrations, homotopy groups, the Hurewicz theorem, vector bundles, characteristic classes, cobordism, and possible further topics at the discretion of the instructor.

Subject:
Algebra
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Behrens, Mark
Analysis I, Fall 2010
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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subject:
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Wehrheim, Katrin
Analysis II, Fall 2005
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Continues 18.100, in the direction of manifolds and global analysis. Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, differential forms, n-dimensional version of Stokes' theorem. 18.901 helpful but not required.

Subject:
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Guillemin, Victor
Applied Calculus
Conditions of Use:
No Strings Attached
Rating

Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

Subject:
Calculus
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Dale Hoffman
David Lippman
Shana Calaway
Applied Geometric Algebra, Spring 2009
Conditions of Use:
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Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976. Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems. The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface below. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

Subject:
Algebra
Physics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Tisza, L
Applied Probability
Conditions of Use:
No Strings Attached
Rating

This is a "first course" in the sense that it presumes no previous course in probability. The units are modules taken from the unpublished text: Paul E. Pfeiffer, ELEMENTS OF APPLIED PROBABILITY, USING MATLAB. The units are numbered as they appear in the text, although of course they may be used in any desired order. For those who wish to use the order of the text, an outline is provided, with indication of which modules contain the material.

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
Rice University
Provider Set:
OpenStax CNX
Author:
Paul E. Pfeiffer
Applied Probability
Conditions of Use:
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Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) is done using Matlab.

Subject:
Statistics and Probability
Material Type:
Full Course
Homework/Assignment
Lecture
Lecture Notes
Reading
Provider:
ArsDigita University
Provider Set:
ArsDigita University
Author:
Rajeev Surati
Tina Kapur
Applied Statistics, Spring 2009
Rating

I designed the course for graduate students who use statistics in their research, plan to use statistics, or need to interpret statistical analyses performed by others. The primary audience are graduate students in the environmental sciences, but the course should benefit just about anyone who is in graduate school in the natural sciences. The course is not designed for those who want a simple overview of statistics; we’ll learn by analyzing real data. This course or equivalent is required for UMB Biology and EEOS Ph.D. students. It is a recommended course for several of the intercampus graduate school of marine science program options. 

Subject:
Statistics and Probability
Material Type:
Full Course
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
 Eugene Gallagher
Are All Stars Like The Sun?
Conditions of Use:
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This is an activity about comparing images of the Sun in different wavelengths of light. Learners will examine solar images taken by the SOHO spacecraft to look for differences in the features that are visible in the various wavelengths of light. This activity requires access to the internet to view or print images of the Sun. This is Activity 7 of the Sun As a Star afterschool curriculum.

Subject:
Engineering
Mathematics
Material Type:
Activity/Lab
Data Set
Diagram/Illustration
Full Course
Lesson Plan
Provider:
NASA
Provider Set:
NASA Wavelength
Arithmetic for College Students
Conditions of Use:
No Strings Attached
Rating

This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

Subject:
Mathematics
Material Type:
Full Course
Textbook
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
David Lippman
The Art of Counting, Spring 2003
Conditions of Use:
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The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

Subject:
Mathematics
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Stanley, Richard
The Art of the Probable: Literature and Probability, Spring 2008
Conditions of Use:
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The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to): the attempt to quantify or otherwise explain the presence of chance, risk, and contingency in everyday life; the deduction of causes for phenomena that are knowable only in their effects; and, above all, the question of what it means to think and act rationally in an uncertain world. Our course therefore aims to broaden students’ appreciation for and understanding of how literature interacts with--both reflecting upon and contributing to--the scientific understanding of the world. We are just as centrally committed to encouraging students to regard imaginative literature as a unique contribution to knowledge in its own right, and to see literary works of art as objects that demand and richly repay close critical analysis. It is our hope that the course will serve students well if they elect to pursue further work in Literature or other discipline in SHASS, and also enrich or complement their understanding of probability and statistics in other scientific and engineering subjects they elect to take.

Subject:
Arts and Humanities
Literature
Philosophy
Religious Studies
Statistics and Probability
Material Type:
Full Course
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Jackson, Noel
Kibel, Alvin
Raman, Shankar
Basic Math (BPCC Open Campus Math 097)
Rating

This course is a review of basic mathematics skills. Here's what's covered:
-fundamental numeral operations of addition, subtraction, multiplication
division of whole numbers, fractions, and decimals
-ratio and proportion
-percent
-systems of measurement
-an introduction to geometry
NOTE: Open Campus courses are non-credit reviews and tutorials and cannot be used to satisfy requirements in any curriculum at BPCC. (Basic Mathematics Course by Bossier Parish Community College is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Based on a work at http://bpcc.edu/opencampus/index.html.)

Subject:
Mathematics
Material Type:
Full Course
Provider:
Bossier Parish Community College
Author:
Michelle Barnickel
Basic Mathematics
Rating

BPCC Open Campus - Math 097: Basic Mathematics is a review of basic mathematics skills. Here's what's covered: -fundamental numeral operations of addition, subtraction, multiplication division of whole numbers, fractions, and decimals -ratio and proportion -percent -systems of measurement -an introduction to geometry NOTE: Open Campus courses are non-credit reviews and tutorials and cannot be used to satisfy requirements in any curriculum at BPCC.

Subject:
Education
Mathematics
Material Type:
Assessment
Full Course
Lecture
Lesson
Unit of Study
Author:
Allison Martin
Beginning Algebra
Conditions of Use:
Read the Fine Print
Rating

This course is also intended to provide the student with a strong foundation for intermediate algebra and beyond. Upon successful completion of this course, you will be able to: simplify and solve linear equations and expressions including problems with absolute values and applications; solve linear inequalities; find equations of lines; and solve application problems; add, subtract, multiply, and divide various types of polynomials; factor polynomials, and simplify square roots; evaluate, simplify, multiply, divide, add, and subtract rational expressions, and solve basic applications of rational expressions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 001)

Subject:
Algebra
Material Type:
Full Course
Provider:
The Saylor Foundation