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Topology and Analysis Forum

Participate in expert discussion on topology and analysis topics. This includes point-set topology, Real, complex, harmonic and functional analysis. Also measure and integration theory.

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Graduate Aysmptotics : Need help with residues

Oct 26, 2004 · Replies 5 · Oct 26, 2004

Replies: 5

Views: 2K

Undergrad What is the real part of a function like f(z)= √(z)?

Oct 24, 2004 · Replies 7 · Oct 25, 2004

Replies: 7

Views: 13K

Undergrad Solving Complex Equation: z^4 + 1/2(1 - i3^(1/2)) = 0

Oct 24, 2004 · Replies 3 · Oct 24, 2004

Replies: 3

Views: 2K

Graduate What Are the Physical Implications of Complex Numbers in Quantum Mechanics?

Sep 17, 2004 · Replies 20 · Oct 12, 2004

Replies: 20

Views: 4K

High School Is My Approach to Simplifying Complex Fractions Correct?

Oct 7, 2004 · Replies 19 · Oct 12, 2004

Replies: 19

Views: 3K

Undergrad Question:How can I solve the complex equation z^4-2z^2+4=0?

Oct 11, 2004 · Replies 5 · Oct 11, 2004

Replies: 5

Views: 4K

High School What is the relationship between complex numbers and conjugates?

Sep 30, 2004 · Replies 25 · Oct 5, 2004

Replies: 25

Views: 4K

Graduate What Are the Key Concepts and Applications of Topology?

Oct 1, 2004 · Replies 20 · Oct 4, 2004

Replies: 20

Views: 5K

Graduate What is a Klein bottle and its role in mathematics?

Oct 2, 2004 · Replies 1 · Oct 2, 2004

Replies: 1

Views: 3K

Undergrad What is e^(pi*i) = - 1? Learn How to Solve it

Sep 29, 2004 · Replies 4 · Sep 29, 2004

Replies: 4

Views: 2K

Graduate Chess/Math Puzzle: A Topological Approach

Sep 27, 2004 · Replies 25 · Sep 28, 2004

Replies: 25

Views: 4K

Undergrad Complex numbers (5+2i)=SQRT(x+iy)

Sep 26, 2004 · Replies 4 · Sep 26, 2004

Replies: 4

Views: 4K

Graduate Is a Hilbert space over the quaternions separable?

Sep 25, 2004 · Replies 7 · Sep 25, 2004

Replies: 7

Views: 5K

Graduate Interpreting Imaginary Component Amplitudes in Fourier Series

Sep 22, 2004 · Replies 3 · Sep 22, 2004

Replies: 3

Views: 2K

Undergrad Is the Complex Number z on a Circle?

Sep 1, 2004 · Replies 9 · Sep 5, 2004

Replies: 9

Views: 11K

Graduate Complex numbers / cartesian equations etc

Jul 27, 2004 · Replies 8 · Aug 25, 2004

Replies: 8

Views: 9K

High School Real & Imaginary Parts of Complex Signals Explained

Aug 20, 2004 · Replies 5 · Aug 20, 2004

Replies: 5

Views: 4K

Graduate ElementaryFunctions/Exp/06/GraphingOnTheComplexPlane

Aug 10, 2004 · Replies 5 · Aug 11, 2004

Replies: 5

Views: 13K

Graduate Understanding Notation for Hyperbolic Functions with Complex Numbers

Aug 2, 2004 · Replies 9 · Aug 3, 2004

Replies: 9

Views: 3K

Undergrad Calculating (a+bi)^(c+di): How to Find it?

Aug 1, 2004 · Replies 5 · Aug 2, 2004

Replies: 5

Views: 4K

Graduate Discover Topology Interest - Helpful Sites & Resources

Jul 14, 2004 · Replies 5 · Jul 16, 2004

Replies: 5

Views: 2K

Undergrad Distance between two complex numbers

Jun 27, 2004 · Replies 4 · Jun 28, 2004

Replies: 4

Views: 9K

Undergrad Solutions to four complex numbers showing how arg(z) is obtained

Jun 22, 2004 · Replies 17 · Jun 27, 2004

Replies: 17

Views: 13K

Graduate Understanding Stalks and Direct Limits in Algebraic Geometry

Jun 3, 2004 · Replies 11 · Jun 27, 2004

Replies: 11

Views: 6K

Graduate Geometric Arguments for Z1-Z2 in Complex Plane

Jun 25, 2004 · Replies 5 · Jun 26, 2004

Replies: 5

Views: 16K

Undergrad Solve Complex Equations | Helpful Tips for Troublesome Equations

Jun 25, 2004 · Replies 7 · Jun 25, 2004

Replies: 7

Views: 2K

High School Understanding the Science behind the Mysterious Mobius Strip

Jun 11, 2004 · Replies 5 · Jun 11, 2004

Replies: 5

Views: 7K

Graduate Victoria Math Forum: Analysis or Algebra? Let's Discuss!

May 3, 2004 · Replies 4 · May 7, 2004

Replies: 4

Views: 2K

Graduate Small problem, can anyone help?

May 5, 2004 · Replies 1 · May 6, 2004

Replies: 1

Views: 2K

Graduate What are the values of z that satisfy the equation e^z = 1 + sqrt(3)i?

Apr 24, 2004 · Replies 6 · Apr 25, 2004

Replies: 6

Views: 2K

Graduate What is the Purpose of Topology in Mathematics?

Apr 18, 2004 · Replies 3 · Apr 20, 2004

Replies: 3

Views: 2K

Graduate Solution to quddusaliquddus's cont func. questions if you want it

Apr 6, 2004 · Replies 4 · Apr 7, 2004

Replies: 4

Views: 2K

Graduate Determining All Continuous Functions s.t.

Apr 6, 2004 · Replies 9 · Apr 6, 2004

Replies: 9

Views: 2K

Undergrad Solve Complex Equation z^2 - (7+i)z + 24 + 7i = 0

Apr 6, 2004 · Replies 6 · Apr 6, 2004

Replies: 6

Views: 3K

Undergrad What are the errors in this complex number equation?

Mar 31, 2004 · Replies 5 · Mar 31, 2004

Replies: 5

Views: 2K

Graduate What are 'inf' and 'sup' and how do they relate to dynamics on time scales?

Mar 3, 2004 · Replies 15 · Mar 5, 2004

Replies: 15

Views: 56K

Graduate Topology: Line Segment Equivalent to a Point

Feb 7, 2004 · Replies 29 · Feb 12, 2004

Replies: 29

Views: 6K

Undergrad Can Arcsin(i2x) be Simplified to iArcsin(2x)?

Feb 12, 2004 · Replies 8 · Feb 12, 2004

Replies: 8

Views: 4K

Undergrad Can "Real Powers" Give You a Rational Number?

Jan 9, 2004 · Replies 2 · Jan 9, 2004

Replies: 2

Views: 2K

High School Understanding Euler's Formula for Complex Numbers - Tips for Evaluating e^ix

Dec 24, 2003 · Replies 10 · Dec 25, 2003

Replies: 10

Views: 6K

Graduate How Does Riemann's Translucent Ball Illustrate Complex Plane Shadows?

Nov 19, 2003 · Replies 4 · Nov 22, 2003

Replies: 4

Views: 3K

Undergrad What? 2 parallel lines meet at infinity?

Oct 6, 2003 · Replies 13 · Oct 28, 2003

Replies: 13

Views: 17K

Undergrad Evaluating complex multiplication?

Oct 26, 2003 · Replies 4 · Oct 26, 2003

Replies: 4

Views: 2K

Undergrad What are the solutions to equations involving complex numbers?

Oct 24, 2003 · Replies 2 · Oct 24, 2003

Replies: 2

Views: 11K

Graduate The notion of continuity applied to sets

Oct 20, 2003 · Replies 4 · Oct 20, 2003

Replies: 4

Views: 3K

Graduate Circle's area and the CH problem

Oct 8, 2003 · Replies 12 · Oct 10, 2003

Replies: 12

Views: 3K

Graduate Decision problem in nonstandard analysis

Oct 2, 2003 · Replies 2 · Oct 2, 2003

Replies: 2

Views: 3K

Graduate Stone-von Neumann theorem & modern analog

Aug 1, 2003 · Replies 21 · Aug 29, 2003

Replies: 21

Views: 8K

Graduate Can |R| be uncountable but not a Continuum?

Aug 5, 2003 · Replies 30 · Aug 10, 2003

2

Replies: 30

Views: 6K

Graduate What are the differences between the filter and net approaches in topology?

Jul 15, 2003 · Replies 3 · Jul 16, 2003

Replies: 3

Views: 6K

Undergrad How do we express complex powers like 21+i in standard form?

Jul 1, 2003 · Replies 3 · Jul 1, 2003

Replies: 3

Views: 8K

Graduate Topology and algebraic topology?

Jun 30, 2003 · Replies 3 · Jun 30, 2003

Replies: 3

Views: 4K

Graduate Can Knots Exist in Higher Dimensions?

Jun 28, 2003 · Replies 1 · Jun 28, 2003

Replies: 1

Views: 3K

Undergrad Complex solution using graph shadows.

May 27, 2003 · Replies 1 · May 27, 2003

Replies: 1

Views: 3K

High School What are complex numbers and how do they differ from real numbers?

Apr 2, 2003 · Replies 2 · Apr 2, 2003

Replies: 2

Views: 3K

Graduate Math Magic Trick: Equidcomposability & the Banach-Tarski Paradox

Mar 26, 2003 · Replies 10 · Mar 30, 2003

Replies: 10

Views: 9K

Graduate What Are the Different Spaces Explored by Physicists and Mathematicians?

Mar 24, 2003 · Replies 3 · Mar 25, 2003

Replies: 3

Views: 4K

Topology and Analysis

Welcome to the Topology forum!

Topology and analysis are two branches of mathematics that investigate the properties of spaces and functions, respectively. Topology is concerned with the study of the properties that remain unchanged under continuous deformations, such as stretching or bending, but not tearing. It explores concepts like continuity, connectedness, and compactness.

Analysis, on the other hand, is focused on understanding the behavior of mathematical functions and sequences. It deals with limits, continuity, differentiation, and integration, providing tools for a detailed examination of functions. Both topology and analysis play integral roles in diverse areas of mathematics and find applications in various scientific and engineering disciplines.

Together, they contribute to a deeper understanding of the structure and properties of mathematical objects.

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