Topology and Analysis Forum

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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.
Undergrad Please explain why z = cosθ + jsinθ in this video.
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MHB Inequality Proof: Fun Problem | z,w <1 | Forum
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MHB Can you please tell me if this question is Correct?
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Undergrad Rethinking Complex Numbers: A New Perspective on Teaching and Understanding
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MHB Solving Complex Expressions for Scientists
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Graduate Can a Non-Monotonic, Bounded Function Have a Limit?
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Graduate How Does Knot Theory Connect with Other Fields and Real-World Applications?
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MHB Ambiguity in the Arc-Tangent Function
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Graduate Where Can I Find Information on Non-Trivial Zeros and Meromorphic Functions?
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MHB What Are the Possible Values of 2^(-i)?
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MHB Can a sequence without a convergent subsequence have a limit of infinity?
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MHB Sum of squares of average change is less than
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Undergrad Finding Amplitude and Phase of Complex Functions
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Graduate Complex conjugates of functions
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Undergrad What is the concept of fractal dimension and how is it computed?
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Graduate Why is this expression bounded by 1?
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Graduate When Does Set-Theoretic Logic Hold for Infinite Sets?
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Graduate Understanding Riemann Surfaces and Their Applications in Complex Analysis
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Graduate How can I prove that this 2D expression is always less than 1 for n≠β?
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MHB Proof of 1+z+Z^2+...+z^n=(1-z^(n+1))/(1-z)
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MHB Find Residues for f(z) at $z=-n$
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Graduate Does L^2 Convergance Imply Convergance of L^2 norms?
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Graduate Challenge VIII: Discontinuities of a function solved by Theorem.
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MHB How many real and non-real roots?
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Graduate The closure of an open set A, strictly bigger than A itself?
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MHB Help with Proof: Sum of Cosines Up to n Terms
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Graduate Unboundness and periodicity for complex trig functions
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Graduate Do Tensor Product Properties Hold in Infinite Dimensional Hilbert Spaces?
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MHB Correspondence between Arc Lengths and Real Numbers in Trigonometry
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MHB Homeomorphism between a cylinder and a plane?
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Graduate Is There a Non-Calculus Method to Prove this Thermodynamic Inequality?
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MHB Which Real Numbers Intersect This Curve at Four Distinct Points?
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Graduate Generalization of Mean Value Theorem for Integrals Needed
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Graduate Some introductory Topology questions
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Graduate A countable subset of an infinite set and the axiom of choice.
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Graduate Lebesgue measure and the Banch-Tarski Paradox
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Graduate How Does Orthogonal Projection Work in L^2 Spaces with a Self-Adjoint Operator?
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Graduate Complex integral is zero but fn. is not analytic
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Graduate Challenge IV: Complex Square Roots, solved by jgens
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Graduate How Can Norm Integration Address Inequality?
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MHB Infinite Product: Showing & Evaluating
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Graduate Bounds on infinite sequences with a known limit
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MHB Irrational numbers forming dense subset
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MHB Problem about finding sup of a set
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Undergrad Proof about complex conjugate of a function
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Graduate Finding large order spherical harmonics
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Graduate What Causes the Complex Number Paradox in Mathematics?
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Graduate Show that an open connected subset of R^2 is path-connected
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Graduate Equivalent conditions for a measurability restriction?
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Graduate Equal partition Integral problem
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Graduate Lipschitz vs uniform continuity.
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Graduate Could we have negative dimensions?
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Graduate Complex analysis book with lots of solved problems?
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MHB Do we have identities for the inverse tangent function for complex numbers?
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Graduate Are Abelian fundamental groups always isomorphic in path connected spaces?
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Graduate Is Every Closed Subset of ##\mathbb{R}^2## the Boundary of Some Set?
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MHB What are the $\rho$ values in the zeros of the Zeta function?
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MHB Liouville's extension of Dirichlet's theorem
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Graduate Can the rational numbers be embedded in a countable complete metric space X?
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MHB Inequality--is there an elegant way to solve this?
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MHB Which Book Should I Choose for Starting Complex Analysis?
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MHB Exact Differential: Show f(z)dz is Exact
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Graduate Why is 4 Colors Sufficient to Color a 2D Map?
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MHB Continuous mapping of compact metric spaces
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Graduate Some questions about topological groups
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Graduate Are Maps on a Sphere Homotopic if They Avoid Antipodal Points?
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Graduate Is the maximum of infinitely many functions continuous on a compact space?
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Graduate Integral Inequality for Measurable Functions
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Graduate Homeomorphism of Unit Circle and XxX Product Space
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Graduate Evaluate Integral of Bessel K Function
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MHB Compactness Theorem: Intersection of Compact Sets
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Graduate Box topology does not preserve first countable
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Graduate Hausdorff Spaces: Does Convergence to One Point Characterize?
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MHB Real & Complex Analysis: Beginner's Guide
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Graduate Does a second countable space have a converging sequence in its closure?
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Graduate Graph of f:[0,1]->R compact <=> f continuous
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Graduate The difference between the limits of two Cauchy Sequences
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Graduate Prove Compact Metric Space is Locally Path Connected
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Graduate Open sets in the product topology
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Graduate Cont image of connected space is connected proof check?
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Graduate A problem about non-separable Hilbert space
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Graduate Find a 2-arguments function from six constraints on its derivatives
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MHB Prove Log Gamma Integral: $\sqrt{2 \pi}$
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Graduate Homeomorphism through cutting and pasting of manifolds
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Graduate Why is the Twin Primes Conjecture still relevant to mathematicians today?
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MHB Lagrange's Identity and Cauhchy-Schwarz Inequality for complex numbers
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MHB Prove 7.81: Contour Integration for Schaum's Outline Series
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Graduate Why Isn't the Sum of Grandi's Series Zero?
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Undergrad A proof regarding Rational numbers
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Graduate Problem in understanding the meaning
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Graduate Matrix-valued analytic function?
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Graduate Analytical solution of an infinite series
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Graduate Residue of Function f(z)=e1/z/(1-z): Guide and Explanation
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Graduate Infinitely differentiable complex functions
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Graduate Dirac Delta Function: Explanation & Usage
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Undergrad Complex Power Operation: Is x^iy Possible?
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Graduate Differentiating delta function composed with a function
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Graduate Interpreting ##\alpha \delta(x)##: Is ##\alpha## at ##x=0##?
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Graduate How Can Abelian Integrals Be Simplified for Beginners?
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MHB Problem 15 section 5.1 from Bartle
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