Math POTW for University Students Forum

POTW Sum of an Alternating Series
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9
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278
POTW Limit of a Nonnegative Continuous Function
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1
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256
POTW Does the Taylor series for arctan converge at x = 1?
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19
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1K
POTW Groups of Prime Power Order
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1
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159
POTW Inequality of Determinants
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10
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715
POTW A Series Converging to a Lipschitz Function
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1
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474
POTW Neumann Boundary Value Problem in a Half Plane
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1
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446
POTW Does the Alternating Binomial Sum Formula Hold for All Positive Integers?
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1
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453
POTW Integration Over a Line in the Complex Plane
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8
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673
POTW Power Sums Limits: Evaluating $\lim_{n\to \infty}$
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3
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615
POTW Solution to a Matrix Quadratic Equation
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4
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646
POTW Hölder Continuous Maps from ##R## to a Metric Space
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3
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682
POTW Find Limit of $$\frac{x}{e} - \left(\frac{x}{x+1}\right)^x$$ at Infinity
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3
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600
POTW An Integral with Fractional Part
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3
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641
POTW Product of Two Finite Cyclic Groups
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1
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553
POTW Prove Hermitian Matrices Satisfy ##H^2 = H^\dagger H##
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22
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1K
POTW Fourier Series on the Unit Interval
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3
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817
POTW A Test for Absolute Convergence of a Series
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1
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560
POTW A Linear Operator with Trace Condition
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1
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648
POTW Ramanujan Sums: Showing $c_n(k)$
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3
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693
POTW Definite Integral of a Rational Function
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6
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916
POTW Solve Linear System of ODEs: x',y' w/ Initial Conditions x(0),y(0)
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10
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1K
POTW Preservation of Local Compactness
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4
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757
POTW Is the Rank of AB Related to the Ranks of A and B?
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2
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892
POTW Show That the Curve is Straight
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4
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857
POTW Gaussian Integrals in Two Dimensions
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3
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754
POTW Uniformly Continuous Functions on the Real Line
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15
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951
POTW Exponential-Type Integrals
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11
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1K
POTW Expected Value of a Maximum
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14
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2K
POTW Support of a Finitely Generated Module
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7
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1K
POTW Infinite Sequences of Sines
2
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44
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2K
POTW A Modified Basis in an Inner Product Space
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2
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878
POTW Proof of Asymptotic Equality: $\sum_{n=0}^\infty a_n\frac{x^n}{n!} \sim ae^x$
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1
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767
MHB Can a Topological Space Be Homotopy Equivalent to a Cylinder?
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3
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1K
MHB Is $SO(3)$ Path-Connected?
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1
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998
MHB Can Continuity Ensure Infinite Limits in Nested Functions?
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1
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3K
MHB Is Function $f$ Convex if its Hessian Matrix is Positive Semidefinite?
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1
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2K
MHB What is the Unique Linear Functional in $M_n(\Bbb F)$ Satisfying Two Conditions?
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1
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2K
MHB How to prove the convergence of a series with absolute values?
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1
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2K
MHB Can You Evaluate This Tricky Improper Integral?
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1
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2K
MHB How Do You Prove a Point is Critical When a Function is Non-Negative Nearby?
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1
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2K
MHB Show that the equation $2a^3 - 7b^2 = 1$ has no solution over the integers
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1
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986
MHB Is $K$ Contained in the Center of $G$ if $|K|=5$ and $|G|$ is Odd?
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1
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2K
MHB Can You Tackle the Subset Chain Challenge in Math?
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1
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1K
MHB Can Harmonic Functions Agree at All Points in a Bounded Domain?
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1
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3K
MHB Prove the Famous Result: \(\sum_{k = 1}^\infty \frac{1}{k^2} = \frac{\pi^2}{6}\)
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1
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3K
MHB How can you evaluate the integral of cosine raised to the fifth power?
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1
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3K
MHB Why Are There an Odd Number of Elements in a Finite Group Where g^3 Equals 1?
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1
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3K
MHB Can compact Hausdorff sets be expanded by open sets?
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1
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2K
MHB What is the formula for the volume of a solid unit n-sphere in n+1 dimensions?
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1
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2K
MHB Is the Tensor Product of Flat Modules Flat?
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1
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3K
MHB Can You Solve This Linear System of ODE with Initial Conditions?
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1
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2K
MHB Is $g(z)$ holomorphic if $f$ is holomorphic in $G$?
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1
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2K
MHB Is $M$ a Finite Metric Space if $BC(M)$ is a Finite Real Vector Space?
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1
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2K
MHB Do Complex Plane Medians Intersect at Triangle Centroid?
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1
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2K
MHB Can You Tackle This Week's Challenging PDE?
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1
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2K
MHB Is There a Simple Group of Order $2n$ for Odd $n \geq 3$?
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1
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2K
MHB Can You Tackle This Advanced Series Summation Challenge?
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1
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2K
MHB What Are This Week's Math Challenges in POTW #342?
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1
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2K
MHB Is Orientability Preserved by Local Diffeomorphisms?
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1
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2K
MHB Can You Match Partitions from Set A and Subset B?
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1
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2K
MHB How Fast Does the Chain Move Off the Table in POTW #339?
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1
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2K
MHB Can an analytic function on the half plane be represented by an integral?
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1
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1K
MHB How Do You Prove the Inequality Involving Primes and Harmonic Sum for POTW #337?
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1
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2K
MHB Is the one-point compactification of X-S homeomorphic to X/S?
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1
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2K
MHB What is the proof that a commutative ring with prime proper ideals is a field?
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2
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2K
MHB How to Derive g(x) from f(x) Using the Möbius Function?
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1
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2K
MHB What is the solution to this week's POTW?
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1
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1K
MHB Did Ackbach Solve This Week's Advanced Math POTW Correctly?
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1
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1K
MHB How to Prove the Integral Identity in POTW #331?
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2
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2K
MHB How to Submit Solutions for POTW #330?
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1
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2K
MHB Is Any Subgroup of a Finite Group with Smallest Prime Order Divisor Normal?
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1
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2K
MHB Is a dense, locally compact subspace always open in a compact Hausdorff space?
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1
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1K
MHB Why can't $u$ achieve its maximum in the interior of $\Omega$?
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1
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1K
MHB Is a Uniformly Convergent Sequence of Bounded Functions Also Bounded?
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1
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2K
MHB How many subspaces can be formed in a vector space over a finite field?
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1
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2K
MHB Is the Quotient of a Banach Space by a Closed Linear Subspace also Banach?
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1
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1K
MHB Problem Of The Week # 323 - Sep 14, 2018
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1
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1K
MHB Are There Infinite Primes of the Form 4k + 1?
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1
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2K
MHB How Do Nonempty Closed Sets Intersect in Compact Spaces?
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1
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1K
MHB Can You Crack This Vector Identity Challenge?
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2
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1K
MHB What is the Sum of a Series Involving Sine Squared for $0 < x < \pi$?
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1
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2K
MHB How can you prove the number-theoretic equation $\sum_{d|n} \phi(d) = n$?
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1
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2K
MHB What is the Solution to POTW #317?
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1
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2K
MHB Can You Prove This Advanced Mathematical Inequality?
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1
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2K
MHB Is $f$ Constant if Distance Between Points is Raised to a Power Greater than 1?
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1
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2K
MHB How can a rank 1 complex matrix be written as a product of two matrices?
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1
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2K
MHB Is the direct sum of isomorphic commutative rings always equal in size?
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1
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2K
MHB Can Two Solutions of a PDE be Equal with Given Boundary Conditions?
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2
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2K
MHB What is the volume of a pyramid with given side lengths?
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1
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2K
MHB Can any two bounded functions be transformed into a maximum of two functions?
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1
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2K
MHB Given $n$ points in the plane, any listing (permutation) $p_1, p_2,\dots,p_n$
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1
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2K
MHB What values of alpha make these curves tangent?
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1
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2K
MHB John tosses $6$ fair coins, and Mary tosses $5$ fair coins. What is the probability that John gets more "heads" than Mary?
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1
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2K
MHB What is the largest possible radius of a circle contained in a $4$-dimensional hypercube of side length $1?$
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1
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2K
MHB Problem Of The Week # 305 - Apr 10, 2018
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1
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1K
MHB Can one choose a winning team from each day in a round-robin tournament with no repeats?
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1
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2K
MHB Find the locus of a point moving so that the sum of its perpendicular distances from the four lines is constant
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1
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1K
MHB If $k$ is large, the expression above is approximately $\frac{1}{3}$.
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1
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2K
MHB Is the Area and Radius of a Triangle Always Proportional to its Side Lengths?
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1
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2K
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