Math POTW for University Students Forum

POTW Groups of Prime Power Order
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110
POTW Limit of a Nonnegative Continuous Function
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0
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215
POTW Inequality of Determinants
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10
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704
POTW A Series Converging to a Lipschitz Function
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1
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463
POTW Neumann Boundary Value Problem in a Half Plane
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1
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439
POTW Does the Alternating Binomial Sum Formula Hold for All Positive Integers?
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1
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430
POTW Integration Over a Line in the Complex Plane
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8
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652
POTW Does the Taylor series for arctan converge at x = 1?
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18
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1K
POTW Power Sums Limits: Evaluating $\lim_{n\to \infty}$
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3
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599
POTW Solution to a Matrix Quadratic Equation
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4
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631
POTW Hölder Continuous Maps from ##R## to a Metric Space
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3
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672
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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587
POTW An Integral with Fractional Part
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3
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629
POTW Product of Two Finite Cyclic Groups
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1
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537
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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790
POTW A Test for Absolute Convergence of a Series
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1
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548
POTW A Linear Operator with Trace Condition
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1
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638
POTW Ramanujan Sums: Showing $c_n(k)$
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3
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681
POTW Definite Integral of a Rational Function
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6
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901
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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749
POTW Is the Rank of AB Related to the Ranks of A and B?
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2
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881
POTW Show That the Curve is Straight
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4
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851
POTW Gaussian Integrals in Two Dimensions
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3
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738
POTW Uniformly Continuous Functions on the Real Line
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15
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936
POTW Exponential-Type Integrals
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11
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POTW Expected Value of a Maximum
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14
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POTW Support of a Finitely Generated Module
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7
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1K
POTW Infinite Sequences of Sines
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44
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POTW A Modified Basis in an Inner Product Space
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2
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872
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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765
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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987
MHB POTW: Proving $\lim\limits_{x\to \infty} |f(x)| = \infty$
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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 Solve the POTW for October 6, 2020?
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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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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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975
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 POTW: Show Odd No. of Elements $g \in G$ for which $g^3 = 1$
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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 What is the solution to POTW #346 - May 09, 2019?
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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 the problems for this week's 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 What is the velocity as the last link leaves 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 What is the solution to POTW #337 for Jan 15, 2019?
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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 Can you solve POTW #334 - Dec 11, 2018?
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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 Is this week's POTW correctly solved by Ackbach? Read their solution here!
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1
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1K
MHB What is the solution for POTW #331 - Nov 13, 2018?
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2
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2K
MHB What are the Guidelines for Submitting a Solution to 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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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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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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1K
MHB What is the solution to this week's POTW?
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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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MHB What is the Solution to POTW #317?
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1
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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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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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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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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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MHB If $k$ is large, the expression above is approximately $\frac{1}{3}$.
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1
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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
MHB Can you find the limit of a complex function containing integrals and exponents?
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1
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1K
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Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one problem each week at the university math level.

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