Resources

https://en.wikipedia.org/wiki/Mathematics

https://en.wikipedia.org/wiki/Pure_mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications, but pure mathematicians are not primarily motivated by such applications. Instead, the appeal is attributed to the intellectual challenge and aesthetic beauty of working out the logical consequences of basic principles.
- Study of Quantity - Arithmetic
- Study of Structure - Algebra
- Study of Space - Geometry
- Study of Change - Calculus
https://en.wikipedia.org/wiki/Applied_mathematics Applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term applied mathematics also describes the professional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the "formulation, study, and use of mathematical models" in science, engineering, and other areas of mathematical practice.
- Statistic Statistics is the discipline that concerns the collection, organization, analysis, interpretation and presentation of data.
- Computational Mathematics Computational mathematics involves mathematical research in mathematics as well as in areas of science where computing plays a central and essential role, and emphasizes algorithms, numerical methods, and symbolic computations. Computational mathematics proposes and studies methods for solving mathematical problems that are typically too large for human numerical capacity. Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretisation broadly with special concern for rounding errors. Numerical analysis and, more broadly, scientific computing also study non-analytic topics of mathematical science, especially algorithmic matrix and graph theory. Other areas of computational mathematics include computer algebra and symbolic computation. Computational mathematics more specific branches:

Reference

285 Linear Alzebra

Notes from book Mathematics for Computer Science by Eric Lehman, F Thomson Leighton and Albert R Meyer

A proof is a method of establishing truth Mathematics has its own specific notion of “proof.” A mathematical proof of a proposition is a chain of logical deductions leading to the proposition from a base set of axioms.

A proposition is a statement (communication) that is either true or false. For example, both of the following statements are propositions. The first is true, and the second is false. Proposition 1.1.1. 2 + 3 = 5. Proposition 1.1.2. 1 + 1 = 3.

A predicate can be understood as a proposition whose truth depends on the value of one or more variables. For example, we might use the name “P ” for predicate above: P .n/ WWD “n is a perfect square”; and repeat the remarks above by asserting that P .4/ is true, and P .5/ is false. This notation for predicates is confusingly similar to ordinary function notation. If P is a predicate, then P .n/ is either true or false, depending on the value of n. On the other hand, if p is an ordinary function, like n 2 C1, then p.n/ is a numerical quantity. Don’t confuse these two!

Propositions like these that are simply accepted as true are called axioms.

Important true propositions are called theorems. A lemma is a preliminary proposition useful for proving later propositions. A corollary is a proposition that follows in just a few logical steps from a theorem.

The Well Ordering Principle Every nonempty set of nonnegative integers has a smallest element.

anitsh / til

Mathematics #235

Reference

285 Linear Alzebra

Notes from book Mathematics for Computer Science by Eric Lehman, F Thomson Leighton and Albert R Meyer