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Apr 6, 2015 · The idea of linearity is that the structure is conserved with the addition, and the multiplication by a scalar. About linear algebra : If you have two vector spaces E, F E, F over a field K K, a function f: E → F f: E → F is linear if ∀x, y ∈ E, ∀a, b ∈ K ∀ x, y ∈ E, ∀ a, b ∈ K.
The ability to understand and make use of higher mathematical jargon. The ability to make sound judgments on the quality and the validity of a proof. The ability to think through the implications of a definition or a proposition. The ability to fill in the preliminaries on one’s own.
May 2, 2024 · Algebra: The branch of mathematics that substitutes letters for numbers to solve for unknown values. Algorithm: A procedure or set of steps used to solve a mathematical computation. Angle: Two rays sharing the same endpoint (called the angle vertex). Angle Bisector: The line dividing an angle into two equal angles.
- Anne Marie Helmenstine, Ph.D.
- Goals For These Activities
- Understanding A Definition
- Evaluating Definitions
- Writing Definitions
- Creating New Definitions to Create New Problems
To discuss the structure and purpose of definitionsTo teach the skills needed to interpret definitionsTo provide practice writing definitionsStudents need to learn how to read mathematical literature (see Reading Technical Literature in the Getting Informationsection). Because definitions are brief, yet rich in content, they are a good place to start teaching the habits that make for successful understanding of dense mathematical writing. Provide the following definition to the class: N...
Definitions A, D, F, and G all satisfactorily distinguish convex polygons from their non-convex brethren. Which version of a definition mathematicians choose to use is influenced by several considerations. The class should discuss the following questions: 1. Which of the four definitions that work is best? Why? (Students may note that some are clea...
The above activities highlight the value of clearly written and tested definitions. It is instructive for students to attempt writing their own definitions of familiar objects or concepts. Once they understand that creating any definition can be challenging, they are more likely to appreciate the effort required in creating good mathematical defini...
New definitions are an invitation to new problems. Students looking for new questions to pursue should try defining new objects, properties, or relationships. Give your class the definitions of "semicenter" and "semicentral": You can ask them to draw figures that are and are not semicentral. For semicentral shapes, have them identify (e.g., color i...
Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much of this uses common English words, but with a specific non-obvious meaning when used in a mathematical sense. Some phrases, like "in general", appear below in more than one section.
This is a common alternate form of the symbol " =Def = D e f. ", the latter having first appeared in the 1894 book Logica Matematica by logician Cesare Burali-Forti (1861--1931). Other common alternate forms of the symbol " =Def = D e f. " include " def = = d e f. " and " ≡ ≡.
Basic Math Definitions is a webpage that provides easy-to-understand definitions of basic math terms.
