This interactive lesson covers the Mathematics Vision Projects lesson Composing and Decomposing. It helps develop an understanding of composing functions.Materials remixed from the Mathematics Vision Project.
This 11-minute video lesson introduces conic sections.
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.
Functional analysis helps us study and solve both linear and nonlinear problems posed on a normed space that is no longer finite-dimensional, a situation that arises very naturally in many concrete problems. Topics include normed spaces, completeness, functionals, the Hahn-Banach Theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of Lᵖ spaces; Hilbert spaces; compact and self-adjoint operators; and the Spectral Theorem.
This lesson is an introduction to learning to graph linear equations written in Slope-Intercept Form. It was written for the Beginning Algebra 1 student.
This course is devoted to the theory of Lie Groups with emphasis on its connections with Differential Geometry. The text for this class is Differential Geometry, Lie Groups and Symmetric Spaces by Sigurdur Helgason (American Mathematical Society, 2001).
Much of the course material is based on Chapter I (first half) and Chapter II of the text. The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces.
This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations and direct and iterative methods in linear algebra.
This course offers an advanced introduction to numerical analysis, with a focus on accuracy and efficiency of numerical algorithms. Topics include sparse-matrix/iterative and dense-matrix algorithms in numerical linear algebra (for linear systems and eigenproblems), floating-point arithmetic, backwards error analysis, conditioning, and stability. Other computational topics (e.g., numerical integration or nonlinear optimization) are also surveyed.
The goal of this course is to give an undergraduate-level introduction to representation theory (of groups, Lie algebras, and associative algebras). Representation theory is an area of mathematics which, roughly speaking, studies symmetry in linear spaces.
Introductory Algebra is the second of three classes in the developmental mathematics sequence. It provides a development of concepts of variables, expressions, and equations using symbolic algebra to represent primarily linear relationships both graphically and analytically. The concept of function will be developed for the application of linear equations and concepts of dependent and independent variable. Students will also learn to solve simultaneous linear equations as well as how to construct linear equations from slope and point information. Application problems will include geometric figure quantities, ratio and proportion, direct and indirect variation, and conversion of units. Finding the greatest common factor of a polynomial will also be included. The emphasis of the three semester sequence is fortification of mental calculation power with minimum reliance on digital calculation.
Short Description:
This textbook is aligned with the British Columbia Adult Basic Education learning outcomes for Mathematics: Intermediate Level Algebra. The textbook introduces the fundamental concepts of algebra, geometry, and trigonometry while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
Long Description:
This textbook is aligned with the British Columbia Adult Basic Education learning outcomes for Mathematics: Intermediate Level Algebra. The textbook introduces the fundamental concepts of algebra, geometry, and trigonometry while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
Word Count: 166774
ISBN: 978-1-77420-095-7
(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)
This workbook was created by mathematics instructors at Scottsdale Community College in Scottsdale, Arizona. It is designed to lead students through Introductory Algebra, and to help them develop a deep understanding of the concepts. The included curriculum is broken into twelve lessons. 303 pages. Also contains links to video mini-lessons.
A community college level textbook that provides non-STEM students with a high-quality and academically rigorous book.
In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution." The activity closes by asking students to apply what they've learned to similar situations.
Khan Academy video tutorial. After Linear Equations 2.
We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might be wondering, is there the equivalent of matrix division? And before we get into that, let me introduce some concepts to you. And then we'll see that there is something that maybe isn't exactly division, but it's analogous to it.
This animation from KET's distance learning physics course demonstrates the mathematical formula for a scientific law as it applies to light.
Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Created by Sal Khan.
This is the first unit in the Algebra II curriculum and is fundamental for the rest of the year. During this course students study many different functions and their key features. Students will compare, contrast, and make generalizations about these functions using the key features and proper notation. This unit ensures that students can identify each type of key feature properly throughout the rest of the year.Objectives: Students will express and interpret intervals using both interval and inequality notation.Students will be able to express the domain and range of graphs using both interval and inequality notation.Students will be able to find the x and y intercepts of a function from a graph or from a linear equation.Students will be able to identify extrema, increasing, decreasing and constant intervals of a graph using interval notation.Students will be able to write the end behavior for any given graph.Technology Utilized: ● Desmos - This is an online graphing tool that can be used to make basic graphs as well as premade teacher bundles with student investigations. In this unit I have taken some of the premade investigations and edited them to meet my classroom needs.● Answer Garden - This tool will be used to brainstorm key features at the beginning of the unit and to assess student’s prior knowledge.● Kahoot - This tool is used as a classroom formative assessment. Students must be all on the same question which can also elicit discussion and show misconceptions with instant feedback.● Google Forms - This tool is used for short assessments, exit tickets, and graded homework assignments. The ability for multiple types of questions and self checking quiz option make this an easy way to quickly assess students and give feedback.
This is a SoftChalk lesson designed to help students determine key features of a function such as domain, range, x-intercept, y-intercept, positive intervals, negative intervals, and intervals over which the function may be increasing or decreasing.