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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How Do I Evaluate the Integral \(\int(z^2+1)^2dz\) Over a Cycloid Path?
- Stumped1
- · Replies 7 ·
Expand e^{\frac{z}{z-2}} Laurent Series: z=2
- Stumped1
- · Replies 3 ·
Proving Divergence of Series \sum_{n=1}^{\infty} \frac{1}{n^{1+i}}
- Stumped1
- · Replies 11 ·
Graduate Can Complex Numbers be Compared Using Greater-Than and Less-Than Relations?
- quawa99
- · Replies 1 ·
Proof of tan^(-1z) maclauren series
- Stumped1
- · Replies 1 ·
Graduate Understanding Disks-and-Bands Surfaces: Genus and Boundary Components
- WWGD
- · Replies 2 ·
Graduate Transforming a vector in spherical coordinates
- SupernerdSven
- · Replies 1 ·
Cube root of unity with a huge exponent
- Saitama
- · Replies 10 ·
How can I show with the definition that f is continuous?
- evinda
- · Replies 3 ·
Prove $\lim_{n \to \infty} \sqrt[n]{a_1a_2...a_n} = L$ for Convergent ${a_n}$
- mathgirl1
- · Replies 5 ·
How to Determine Orientation in 3-Dimensional Space?
- Amer
- · Replies 1 ·
Using Residue Calculus For a General Cosine Angle
- shen07
- · Replies 8 ·
Graduate Interpretation of 'homologous to' - Munkres analysis of homology grou
- Math Amateur
- · Replies 12 ·
Graduate Closures of the set of measurable functions
- Fredrik
- · Replies 13 ·
Is the set of Natural Numbers Complete?
- solakis1
- · Replies 25 ·
Inverse map is closed under complementation
- carr1
- · Replies 2 ·
Undergrad Complex Analysis and vector calculus
- Avatrin
- · Replies 19 ·
Graduate Homology of Connected Sum of Two Projective Planes, P^2 # P^2
- Math Amateur
- · Replies 4 ·
(f_n) converges pointwise to a continuous f
- evinda
- · Replies 5 ·
Does \(g \circ f_n \to g \circ f\) Uniformly on \(A\)?
- evinda
- · Replies 6 ·
Real life phenomenon that can be modeled by this curve?
- das1
- · Replies 5 ·
How to Calculate Matrix Norm in a Banach Space?
- kalish1
- · Replies 3 ·
Graduate Question on holomorphic functions
- disregardthat
- · Replies 4 ·
Graduate Homology Groups of the Klein Bottle
- Math Amateur
- · Replies 1 ·
Why Do the Points from the Mean Value Theorem Depend on Both n and x?
- evinda
- · Replies 2 ·
Graduate Does If f be a Measurable Function Imply Finite ∫|f|dm?
- Funky1981
- · Replies 8 ·
Does $(1+\frac{x}{n})^n$ Uniformly Converge to $e^x$ on Different Intervals?
- evinda
- · Replies 3 ·
Can a Function and Its Inverse Prove an Integral Inequality?
- evinda
- · Replies 10 ·
Proving Existence of Equal Values in Continuous Functions with Equal Integrals
- evinda
- · Replies 19 ·
Graduate 2D slice of a 6D Calabi-Yau manifold , and other?
- Spinnor
- · Replies 7 ·
Graduate Proof of Identity Theorem: Understanding G is Non-Empty
- disregardthat
- · Replies 9 ·
Graduate Geometric Derivation of the Complex D-Bar Operator
- bolbteppa
- · Replies 1 ·
Riemann Integral: Proving $\int_a^b f = \int_a^c f + \int_c^b f$
- evinda
- · Replies 3 ·
Graduate What is the Topology of a Tangent Bundle?
- MattRob
- · Replies 6 ·
Show that f+g is integrable and find its value
- evinda
- · Replies 2 ·
Show that f is uniformly continuous
- evinda
- · Replies 6 ·
Graduate Why Must Any 2-Cycle of the 2D Torus Be of the Form pγ?
- Math Amateur
- · Replies 4 ·
What is the Branch Cut for log(z)?
- Amer
- · Replies 2 ·
Prove Riemann Integrability: Let f:[0,1]->R
- mathster
- · Replies 2 ·
Series Convergence: Showing Convergence & Sum Equivalence
- mathgirl1
- · Replies 6 ·
Complex numbers and area of octagon
- Saitama
- · Replies 14 ·
No Non-Constant Entire Function $f(z)$ with $Re(f(z))<0$
- Amer
- · Replies 3 ·
Graduate Functionla Analysis separability
- Funky1981
- · Replies 2 ·
Graduate Understanding Saturated Sets in Quotient Maps
- hideelo
- · Replies 4 ·
Graduate Complex Sin value greater than 1
- tim9000
- · Replies 12 ·
Graduate The a set is open iff its complement is closed?
- wotanub
- · Replies 9 ·
Complete Metric Space: X, d | Analysis/Explanation
- shen07
- · Replies 3 ·
Graduate Is R^3 Equivalent to E^3 in Euclidean Space?
- BHL 20
- · Replies 6 ·
Show that the limit of f is equal to y
- evinda
- · Replies 2 ·
Does the function $f_n(x)$ converge pointwise to zero on $(0,+\infty)$?
- evinda
- · Replies 6 ·
How can I find a sequence of functions satisfying certain properties?
- evinda
- · Replies 2 ·
Graduate Fourier series representation for trigonometric and complex form base
- onceinalifetim
- · Replies 1 ·
Is $f(z) = \sin(z)/z$ an analytic function on the complex plane?
- Amer
- · Replies 7 ·
Map of Area Bounded by y=5x & y=-3x in Upper Plane
- Amer
- · Replies 1 ·
Does the Intermediate Value Theorem Apply If h(a) and h(b) Have Opposite Signs?
- TheDougheyMan
- · Replies 3 ·
Why is (x,e_i) a zero sequence?
- mathmari
- · Replies 2 ·
Graduate Cauchy's differintegral formula
- Jhenrique
- · Replies 2 ·
Contraction Map: Proving $f(x)$ is a Contraction
- onie mti
- · Replies 1 ·
Graduate What is the Condition for Antiholomorphism?
- Jhenrique
- · Replies 2 ·
Solving a Functional Equation Problem: Finding f(3)-f(0)
- Saitama
- · Replies 4 ·
Graduate Proof of equality of diameter of a set and its closure
- chipotleaway
- · Replies 3 ·
Graduate Mobius Band as a Quotient Topology
- Math Amateur
- · Replies 1 ·
Graduate Fundamental groups and arcwise connected spaces.
- center o bass
- · Replies 4 ·
Closed infinite orthonormal system
- mathmari
- · Replies 2 ·
Undergrad Circles vs an infinitely n-sided polygon.
- serp777
- · Replies 20 ·
Is $f_n(x_n) \to f(x)$ Given $f_n \to f$ Uniformly and $x_n \to x$?
- evinda
- · Replies 2 ·
Working on lipschitz function and contraction map
- simo1
- · Replies 1 ·
Graduate Torus T^2 homeomorphic to S^1 x S^1
- Math Amateur
- · Replies 1 ·
Proving |f(x)-f(y)| ≤ K ||x-y|| for f:R^2→R
- onie mti
- · Replies 4 ·
Graduate Simple topology problem involving continuity
- Math Amateur
- · Replies 3 ·
Graduate Convolution with Complex-Valued Functions: Applications and Limitations
- mnb96
- · Replies 4 ·
Graduate What the following statement exactly mean?
- lee.spi
- · Replies 4 ·
Undergrad Raising to half power = PRINCIPAL square root?
- perishingtardi
- · Replies 2 ·
Graduate Why Banach Spaces Are Important: A Fellow Student's Question
- Paalfaal
- · Replies 13 ·
Why is the Infimum of f in Any Subinterval Equal to 0?
- evinda
- · Replies 3 ·
Graduate Lebesgue measure in lower dimensional space
- Shaji D R
- · Replies 12 ·
Graduate Inverse of the adjoint of the shift operator
- Likemath2014
- · Replies 3 ·
Spectral decomposition of compact operators
- Fermat1
- · Replies 1 ·
Graduate Dividing Sets in Contact Structures, and Induced Orientations
- WWGD
- · Replies 1 ·
Graduate Constructing Atlases: Understanding Topology for GR Class
- black_hole
- · Replies 9 ·
About open sets in a metric space.
- eraldcoil1
- · Replies 1 ·
Inverse Laplace transform question
- Dustinsfl
- · Replies 1 ·
What does zero at infinity mean?
- Dustinsfl
- · Replies 1 ·
Region of Convergence: Re${s} > -3 for $\beta$
- Dustinsfl
- · Replies 3 ·
Value of Sigma such that the integral converges
- Dustinsfl
- · Replies 7 ·
How can I show that the function is continuous at [0,1)U(1,2]?
- mathmari
- · Replies 15 ·
Graduate Are residues useful for proper integrals?
- jinawee
- · Replies 5 ·
Graduate Solving the Branch Cut Question on f(z) = arccot(z)
- FelixHelix
- · Replies 4 ·
Graduate How to Prove Existence of Integer n in Dedekind Cut Using Archimedean Property?
- Shaji D R
- · Replies 1 ·
Graduate Gamma Function and the Euler-Mascheroni Constant
- epr1990
- · Replies 8 ·
Why Choose Specific Partitions in Integration Proofs?
- evinda
- · Replies 2 ·
Graduate What does it mean to use the integrator as an average?
- sammycaps
- · Replies 1 ·
Graduate Challenge 14: Smooth is not enough
- Office_Shredder
- · Replies 7 ·
Integral Properties of $f^2$: Boundedness?
- evinda
- · Replies 6 ·
Find a real number for a continuous function
- Maxers99
- · Replies 5 ·
Graduate Is a Metric Space with Infinite Distance Totally Bounded?
- johnqwertyful
- · Replies 3 ·
How Does the Linearity of Integration Work for Sum of Functions?
- evinda
- · Replies 12 ·
Understanding and Applying Dirichlet's Conditions for |x| on [-\pi, \pi]
- Suvadip
- · Replies 1 ·
Graduate Test functions for tempered distributions: analytic?
- jasonRF
- · Replies 3 ·