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### Algebra: Ratios and proportions

Khan Academy Free Closed [?] Mathematics Algebra College algebra Ratios and proportions

What ratios and proportions are. Using them to solve problems in the real world. Ratio problem with basic algebra (new HD). Writing proportions. Writing proportions. Find an Unknown in a Proportion. Find an Unknown in a Proportion 2. Proportions 1. Proportions 2 exercise examples. Proportions 2. Constructing proportions to solve application problems. Constructing proportions to solve application problems. The Golden Ratio. Advanced ratio problems. More advanced ratio problem--with Algebra (HD version). Another Take on the Rate Problem. Alternate Solution to Ratio Problem (HD Version). Mountain height word problem. Ratio problem with basic algebra (new HD). Writing proportions. Writing proportions. Find an Unknown in a Proportion. Find an Unknown in a Proportion 2. Proportions 1. Proportions 2 exercise examples. Proportions 2. Constructing proportions to solve application problems. Constructing proportions to solve application problems. The Golden Ratio. Advanced ratio problems. More advanced ratio problem--with Algebra (HD version). Another Take on the Rate Problem. Alternate Solution to Ratio Problem (HD Version). Mountain height word problem.

### Algebra: Systems of equations and inequalities

Khan Academy Free Closed [?] Mathematics Algebra College algebra Systems of equations and inequalities

### Algebraic Combinatorics

Starts : 2009-02-01
MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

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.

### Algebraic Geometry (Fall 2015)

Starts : 2015-09-01
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This is the first semester of a two-semester sequence on Algebraic Geometry. The goal of the course is to introduce the basic notions and techniques of modern algebraic geometry. It covers fundamental notions and results about algebraic varieties over an algebraically closed field; relations between complex algebraic varieties and complex analytic varieties; and examples with emphasis on algebraic curves and surfaces. This course is an introduction to the language of schemes and properties of morphisms.

### Algebraic Geometry (Spring 2009)

Starts : 2009-02-01
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

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.

### Algebraic Techniques and Semidefinite Optimization

Starts : 2006-02-01
MIT OpenCourseWare (OCW) Free Computer Sciences Electrical Engineering and Computer Science Graduate MIT OpenCourseWare

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.

### Algebraic Topology

Starts : 2006-09-01
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

This course is a first course in algebraic topology. The emphasis is on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.

### Algebraic Topology II

Starts : 2006-02-01
MIT OpenCourseWare (OCW) Free Mathematics Graduate MIT OpenCourseWare

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.

### Applications of Linear Algebra Part 1

Starts : 2015-02-23
edX Free Closed [?] English Computer Science Data Analysis & Statistics DavidsonX EdX Math

From simulating complex phenomenon on supercomputers to storing the coordinates needed in modern 3D printing, data is a huge and growing part of our world. A major tool to manipulate and study this data is linear algebra. This course is part 1 of a 2-part course.  In this part, we’ll learn basics of matrix algebra with an emphasis on application. This class has a focus on computer graphics while also containing examples in data mining. We’ll learn to make an image transparent, fade from one image to another, and rotate a 3D wireframe model. We’ll also mine data; for example, we will find similar movies that one might enjoy seeing. In the topic of sports ranking, we’ll be ready to participate in March Madness and submit our own mathematically generated brackets to compete against millions of others. The lectures are developed to encourage you to explore and create your own ideas either through your own programming but also with online tools developed for the course. Come to this course ready to investigate your own ideas.

Courses offered via edX.org are not eligible for academic credit from Davidson College. A passing score in a DavidsonX course(s) will only be eligible for a verified certificate generated by edX.org.

### Applications of Linear Algebra Part 2

Starts : 2015-04-06
edX Free Closed [?] English Computer Science Data Analysis & Statistics DavidsonX EdX Math

Our world is in a data deluge with ever increasing sizes of datasets. Linear algebra is a tool to manage and analyze such data.

This course is part 2 of a 2-part course, with this part extending smoothly from the first. Note, however, that part 1, is not a prerequisite for part 2. In this part of the course, we'll develop the linear algebra more fully than part 1. This class has a focus on data mining with some applications of computer graphics. We'll discuss, in further depth than part 1, sports ranking and ways to rate teams from thousands of games. We’ll apply the methods to March Madness. We'll also learn methods behind web search, utilized by such companies as Google.  We'll also learn to cluster data to find similar groups and also how to compress images to lower the amount of storage used to store them. The tools that we learn can be applied to applications of your interest.  For instance, clustering data to find similar movies can be applied to find similar songs or friends. So, come to this course ready to investigate your own ideas.

Courses offered via edX.org are not eligible for academic credit from Davidson College. A passing score in a DavidsonX course(s) will only be eligible for a verified certificate generated by edX.org.

### Arithmetic and pre-algebra: Addition and subtraction

Khan Academy Free Closed [?] Mathematics Addition and subtraction Arithmetic Arithmetic and Pre-Algebra

### Arithmetic and pre-algebra: Applying mathematical reasoning

Khan Academy Free Closed [?] Mathematics Applying mathematical reasoning Arithmetic Arithmetic and Pre-Algebra

### Arithmetic and pre-algebra: Arithmetic properties

Khan Academy Free Closed [?] Mathematics Arithmetic Arithmetic and Pre-Algebra Arithmetic properties

This tutorial will help us make sure we can go deep on arithmetic. We'll explore various ways to represent whole numbers, place value, order of operations, rounding and various other properties of arithmetic. Introduction to Order of Operations. Order of Operations. Order of Operations 1. More Complicated Order of Operations Example. Order of Operations examples. Order of operations. Place Value 1. Place Value 2. Place Value 3. Place value. Representing numbers. Representing numbers. Comparing place values. Understanding place value 1 exercise. Understanding place value 1. Place value relationships example. Rounding Whole Numbers 1. Rounding Whole Numbers 2. Rounding Whole Numbers 3. Rounding whole numbers. The Distributive Property. The Distributive Property 2. Distributive Property Example 1. Distributive property exercise. Distributive property. Counting 1 exercise. Counting 1. Regrouping numbers intro various place values. Comparing whole number place values. Largest possible number from 4 digits example. Understanding whole number representations. Recognizing irrational numbers. Recognizing rational and irrational numbers. Regrouping whole numbers. Regrouping whole numbers example 1. Regrouping whole numbers example 2. Regrouping whole numbers. Commutative Law of Addition. Commutative Property for Addition. Commutative Law of Multiplication. Associative Law of Addition. Associative Law of Multiplication. CA Algebra I: Number Properties and Absolute Value. Properties of numbers 1. Number properties terminology 1. Identity Property of 1. Identity property of 1 (second example). Identity property of 0. Inverse Property of Addition. Inverse Property of Multiplication. Properties of numbers 2. Introduction to Order of Operations. Order of Operations. Order of Operations 1. More Complicated Order of Operations Example. Order of Operations examples. Order of operations. Place Value 1. Place Value 2. Place Value 3. Place value. Representing numbers. Representing numbers. Comparing place values. Understanding place value 1 exercise. Understanding place value 1. Place value relationships example. Rounding Whole Numbers 1. Rounding Whole Numbers 2. Rounding Whole Numbers 3. Rounding whole numbers. The Distributive Property. The Distributive Property 2. Distributive Property Example 1. Distributive property exercise. Distributive property. Counting 1 exercise. Counting 1. Regrouping numbers intro various place values. Comparing whole number place values. Largest possible number from 4 digits example. Understanding whole number representations. Recognizing irrational numbers. Recognizing rational and irrational numbers. Regrouping whole numbers. Regrouping whole numbers example 1. Regrouping whole numbers example 2. Regrouping whole numbers. Commutative Law of Addition. Commutative Property for Addition. Commutative Law of Multiplication. Associative Law of Addition. Associative Law of Multiplication. CA Algebra I: Number Properties and Absolute Value. Properties of numbers 1. Number properties terminology 1. Identity Property of 1. Identity property of 1 (second example). Identity property of 0. Inverse Property of Addition. Inverse Property of Multiplication. Properties of numbers 2.

### Arithmetic and pre-algebra: Decimals

Khan Academy Free Closed [?] Mathematics Arithmetic Arithmetic and Pre-Algebra Decimals

### Arithmetic and Pre-Algebra: Exponents (basic)

Khan Academy Free Closed [?] Mathematics Arithmetic and Pre-Algebra Exponents (basic) History of Math

Understanding and solving exponents without algebra. Understanding Exponents. Understanding Exponents 2. Level 1 Exponents. Level 2 Exponents. Level 3 exponents. Exponent Rules Part 1. Exponent Rules Part 2.

### Arithmetic and pre-algebra: Exponents, radicals, and scientific notation

Khan Academy Free Closed [?] Mathematics Arithmetic Arithmetic and Pre-Algebra Exponents Radicals Scientific notation

### Arithmetic and pre-algebra: Factors and multiples

Khan Academy Free Closed [?] Mathematics Arithmetic and Pre-Algebra Factors and multiples History of Math

Understanding and finding factors and multiples. After these videos, you'll be ready for fractions. Divisibility Tests for 2, 3, 4, 5, 6, 9, 10. Recognizing Divisibility. The Why of the 3 Divisibility Rule. The Why of the 9 Divisibility Rule. Divisibility tests. Finding Factors of a Number. Finding factors and multiples. Divisibility 0.5. Divisibility Intuition. Divisibility intuition. Prime Numbers. Recognizing Prime Numbers. Prime numbers. Composite numbers. Prime Factorization. Prime factorization exercise. Prime factorization. The fundamental theorem of arithmetic. The fundamental theorem of arithmetic. Common Divisibility Examples. Divisibility. Least common multiple exercise. Least common multiple exercise 2. Least Common Multiple (LCM). Old Least Common Multiple. Least common multiple. Greatest common divisor factor exercise. Greatest Common Divisor. Greatest common divisor. LCM and GCF (greatest common factor) word problems. LCM and GCD word problems. Divisibility Tests for 2, 3, 4, 5, 6, 9, 10. Recognizing Divisibility. The Why of the 3 Divisibility Rule. The Why of the 9 Divisibility Rule. Divisibility tests. Finding Factors of a Number. Finding factors and multiples. Divisibility 0.5. Divisibility Intuition. Divisibility intuition. Prime Numbers. Recognizing Prime Numbers. Prime numbers. Composite numbers. Prime Factorization. Prime factorization exercise. Prime factorization. The fundamental theorem of arithmetic. The fundamental theorem of arithmetic. Common Divisibility Examples. Divisibility. Least common multiple exercise. Least common multiple exercise 2. Least Common Multiple (LCM). Old Least Common Multiple. Least common multiple. Greatest common divisor factor exercise. Greatest Common Divisor. Greatest common divisor. LCM and GCF (greatest common factor) word problems. LCM and GCD word problems.

### Arithmetic and pre-algebra: Fractions

Khan Academy Free Closed [?] Mathematics Arithmetic Arithmetic and Pre-Algebra Fractions