Alexis Sorensen
Kant Final
James Griffith
1:30-3:00(T/TH)
11/17/12
Pure Mathematics
Immanuel Kant, a Prussian philosopher during the 1700s, examined the basis of human knowledge and its existence. Through rationalism and empiricism, Kant developed an individual model that supported the concept of pure mathematics. Kant’s logic allowed him to prove concepts that appeared unable to be proven. Pure mathematics, as an a priori cognition, can be considered to be an example of a concept that may have seemed unable to be supported through facts (Rohlf).

Mathematical principals, all consist of concepts that develop from intuitions. However, these intuitions are not able to develop as a result of prior experience. Fortunately, it is possible to intuit something a priori. An intuition of an object can occur before the actual experience of the given object occurs. One’s intuition contains the mere form of a sensory experience (Kant pp. 18-31).

Human beings, through the slightest form of sensuous intuition, are able to intuit things a priori. However, because individuals are only able to know an object as it appears to them personally, they may not be able to perceive the object as it actually exists. Mathematical concepts are constructed from a combination of intuitions, and not an analysis of concepts. Space and time are both examples of pure a priori intuitions (Rohlf). Geometry is derived from the pure intuition of space. The concept of a mathematical number developed from the addition of successive units of time. Therefore, space and time are pure a priori intuitions. Space and time exist in human beings prior to all other intuitions of objects. Therefore, both the concepts of space and time are considered to be prior knowledge of an object as it appears to an observer through the senses (Kant pp. 35-48).

Pure a priori intuition of space and time is the foundation of empirical a posteriori intuition. Synthetic a priori, in regards to mathematics, makes...

...TOK Reflection: Mathematics
To what extent is math relevant to your life and the lives of others you know and how can it become an even more viable area of knowledge.
“In mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the PureMathematics.”
Roger Bacon (1214-1294)
Mathematics: the abstract science of number, quantity, and space; a subject...

...The importance of Mathematics
In such a modern and non-stop developing world nowadays, most people need mathematics as an important tool for their occupation, no matter what it is. Obviously, mathematics plays a vital role in daily use such as architecture, business, clerical work, etc... We even use math to balance our budget, pay bills, check our saving accounts, etc. Math is an important part of our civilization.
Most people using...

...INTRODUCTION
As the greatest Mathematician “GAUSS” has said –“MATHS IS THE QUEEN OF SCIENCE”, maths is truly the guiding force of human soul. Maths is the purest form of study of nature which comprise of a deep and rational comparison of quantities, structures, spaces, nature of change of different inter-relations and much more. Mathematicians seek out various patterns and formulate new conjectures. Mathematicians counter examines the facts by repeated and repeated logical transformations...

...Semi-Detailed Lesson Plan in Mathematics (Transformations)
Level: First Year High School
Subjects: Mathematics, Geometry, Transformations
I. Objectives:
A. To recognize Euclidean transformations.
B. To recognize reflections, translations, and rotations.
C. To prove theorems related to transformations.
D. To solve problems involving transformations.
E. To apply transformations to real-world situations.
F. To create designs using transformations....

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Set (mathematics)
From Wikipedia, the free encyclopedia
This article is about what mathematicians call "intuitive" or "naive" set theory. For a more detailed account, see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory.
An example of a Venn diagram
The intersection of two sets is made up with the objects contained in both sets
In mathematics, a set is a collection of...

...Why study Mathematics?
The main reason for studying mathematics to an advanced level is that it is interesting and enjoyable. People like its challenge, its clarity, and the fact that you know when you are right. The solution of a problem has an excitement and a satisfaction. You will find all these aspects in a university degree course.
You should also be aware of the wide importance of Mathematics, and the way in which it is advancing at a...

...Introduction
Mathematics is an indispensable subject of study. It plays an important role in forming the basis of all other sciences which deal with the material substance of space and time.
What is Mathematics?
Mathematics may be described as the fundamental science. It may be broadly described as the science of space, time and number. The universe exists in space and time, and is constituted of units of matter. To calculate the extension or...

...Zero in Mathematics
Zero as a number is incredibly tricky to deal with. Though zero provides us with some useful mathematical tools, such as calculus, it presents some problems that if approached incorrectly, lead to a breakdown of mathematics as we know it.
Adding, subtracting and multiplying by zero are straightforward.
If c is a real number,
c+0=c
c-0=c
c x 0=0
These facts are widely known and regarded to hold true in every situation.
However,...