maths document

May 11th, 2015
Studypool Tutor
Price: $40 USD

Tutor description

This document gives full solution to the sums and it will help the students to get full and clear information on maths

Word Count: 16672
Showing Page: 1/38
A VIEW OF MATHEMATICSAlain CONNESMathematics is the backbone of modern science and a remarkably efficient sourceof new concepts and tools to understand the reality in which we participate.It plays a basic role in the great new theories of physics of the XXth century suchas general relativity, and quantum mechanics.The nature and inner workings of this mental activity are often misunderstoodor simply ignored even among scientists of other disciplines. They usually onlymake use of rudimentary mathematical tools that were already known in the XIXthcentury and miss completely the strength and depth of the constant evolution ofour mathematical concepts and tools.I was asked to write a general introduction on Mathematics which I ended up doingfrom a rather personal point of view rather than producing the usual endless litanyX did this and Y did that. The evolution of the concept of space in mathematics serves as a unifying theme starting from some of its historical roots andgoing towards more recent developments in which I have been more or less directlyinvolved.Contents1. The Unity of Mathematics2. The concept of Space2.1. Projective geometry2.2. The Angel of Geometry and the Devil of Algebra2.3. Noneuclidean geometry2.4. Symmetries2.5. Line element and Riemannian geometry2.6. Noncommutative geometry2.7. Grothendiecks motives2.8. Topos theory3. Fundamental Tools3.1. Positivity3.2. Cohomology3.3. Calculus3.4. Trace and Index Fo

Review from student

Studypool Student
" Solid work, thanks. "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1829 tutors are online

Other Documents


Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors