## Publications and Research

Article

Summer 8-3-2020

#### Abstract

In mathematics we start, by using discovery method, with small observations and operations, then we look for patterns, algorithms procedures, and furthermore we generalize by writing theorems, formulas, and conclusions. Our intuitive thinking, the needs for solving real-life problems, and curiosity often push us towards research and study more about things that matter to us, especially when we see that problems need to be solved right away. This kind of things have driven people now and back then depended on the era in which they have lived, or they live in. For example: In these days, because of Covid 19 doctors and researchers and other health care organizations, are interested and they are working on collecting data, analyzing, modeling the spread of the virus to track epidemics and make predictions about the progression. While for example, exceedingly early (3400 BC – Mesopotamia) 1 the numerical system was discovered. Everything that is measurable and plays specific role in our lives needs to be well evaluated. For that reason, we need mathematical reasoning and calculations to draw the appropriate conclusions.

Despite what we notice, observe, and we realize by doing some calculations, everything needs proof. We need to make sure that what we state as true statement must be proven as true.

In this article I will discuss some of the most important Proof Methods in Teaching Mathematics

Larson, Ron; Eduards, Bruce, (2016). Book Title. Calculus, Pennsylvania State University, University of Florida: Publisher: Cengage Learning

Johnsonbaugh, Richard, Eighth Edition, Book Title: Discrete Mathematics, DePaul University, Chicago

Footnotes

1[I have used here many of the textbooks such as Calculus, Precalculus, Algebra, Discrete Mathematics etc. I have read a lot of articles and researching papers. I also, have use my long- time experience of teaching different levels of Mathematics.]

Here are only a few links to the resources used:

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

https://www.sciencedaily.com/releases/2020/03/200325110855.htm

https://www.cs.sfu.ca/~ggbaker/zju/math/proof.html#disprove

https://mathbitsnotebook.com/Geometry/BasicTerms/BTproofs.html

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

http://web.mnstate.edu/jamesju/Fall2015/Content/M311ProofsIntro.pdf

https://openstax.org/books/calculus-volume-1/pages/2-4-continuity

https://www.birmingham.ac.uk/Documents/college-eps/college/stem/Student-Summer-Education-Internships/Proof-and-Reasoning.pdf

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