Math Problem of the Week Forum

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High School Can You Factorize This Complex Algebraic Expression?
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High School How Can the Product of Factorials from 1 to 15 Be Expressed as \(A^2B!\)?
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Undergrad Problem of the Week #177 - October 20, 2015
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Is it possible to form six prime numbers using three distinct digits?
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Undergrad Can k[x1,...,xn] be Isomorphically Mapped to k[x1]⊗k⋯⊗k[xn]?
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Is There a Trio of Nations with the Same Relationship in This Math Challenge?
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High School Can You Solve This Quartic Equation with Roots Involving Square-Free Integers?
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Undergrad What is the Radon-Nikodym derivative of the pushforward of a function?
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How do I solve the Diophantine equation $4x+51y=9$?
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High School Can you prove this fractional equality?
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Undergrad Is the Lie derivative of a smooth vector field equal to the Lie bracket field?
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What is the significance of a group with no proper subgroups?
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High School How Do You Solve $\cot x \cdot \cot(x+y)$ Given $\cos y = 17\cos(2x+y)$?
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High School Can You Crack the Trigonometric Integration Challenge?
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Undergrad How Do You Determine the Degree of the Field Extension K/L in POTW #173?
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How Can You Solve the Simply Supported Beam Equations?
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Undergrad What is the Pointwise Limit of This Sequence of Integral Functions?
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Can You Solve the Non-Uniform Convergence Integral Challenge?
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High School How Does a Double Root Lead to the Equation $108a^5=-3125b^3$?
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What is the Shortest Path for a Spider to Capture a Fly on a Cube?
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Undergrad What Is the Pushforward of the Inversion Mapping at the Identity of a Lie Group?
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High School Unit Circle Chord Probability: POTW #180 Sept. 7, 2015
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Undergrad Is X Always Commutative with Y in Matrix Invariance?
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What is the inverse of the function f(x)=x^3-3x for different intervals?
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High School How Do You Calculate the Floor of 2√xn for the Given Sequence?
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Undergrad How Can You Prove This Complex Integral Equals $\frac{\sqrt{6\pi}}{4}$?
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What are Lagrange's equations of motion for a pendulum suspended by a spring?
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High School How to Evaluate √1061520150601 Without a Calculator?
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High School How Do You Calculate $ab+bc+ca$ Using Trigonometric Identities?
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Is the Mapping (x,y) -> (u^2-v^2,2uv) Conformal Everywhere Except the Origin?
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Undergrad Can You Solve the Challenging Math Problem from POTW #168?
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Undergrad Is $p$ irreducible in $\Bbb Z[(-1 + i\sqrt{3})/2]$ if $p \equiv 2\pmod{3}$?
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How Can You Tile an $8 \times 8$ Chessboard with L-Shaped Pieces?
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High School How Do You Evaluate the Sum of Reciprocal Factorial Pairs?
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What is the solution to this challenging nonlinear PDE?
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Undergrad Why does the sequence $w_n = T^n(0)$ tend to infinity if $|z_0| > 2$?
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High School Can You Solve This Intriguing Real Numbers Equation?
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Undergrad What is the connection form matrix of a surface of revolution?
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Can Even Numbers Be Written as the Sum of Two Primes?
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High School Do $x, y, z$ Meet the Triangle Inequality Conditions?
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Undergrad What is the Integral of a Trigonometric Expression with Positive Constants?
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Which Fairies are Telling the Truth?
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High School What Are All the Real Solutions to the Equation \(a^4+b^4+c^4+1=4abc\)?
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What is the solution to Problem of the Week #172?
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Undergrad Can you determine the stability of a fixed point in a system of ODEs?
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High School Can $\sqrt{k-1} + \sqrt{k+1}$ Be a Rational Number for Any Integer k?
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What is the integral of x^2 over 1+x^10 from 0 to infinity?
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Undergrad Can a normal subgroup of a transitive group also be transitive?
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High School How Do You Maximize This Complex Expression With Given Constraints?
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Undergrad What is the Limit of the Bessel Function as x Goes to Infinity?
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High School How Do You Find the Coefficient \( a_2 \) in a Polynomial Transformation?
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What is the condition for $E$ in the time-independent Schrödinger equation?
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How many walks of length $n$ can you find on this graph?
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High School Real Numbers Inequality Proof: x+y+z > (|x|+|y|+|z|)/3
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Undergrad How can you prove the Laplace transform of a periodic function with an integral?
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High School How Do You Solve Complex Root Expressions in Polynomial Equations?
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Undergrad Is the Endomorphism Ring of a Finite Dimensional Vector Space Dedekind Finite?
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Is $EFGH$ a parallelogram in quadrilateral $ABCD$?
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Undergrad Is it Possible for a Random Variable to Have a Variance of Zero?
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What is the Maximum Number of Equivalence Classes for the Eight Queens Problem?
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High School Prove One Root in Interval (0,1) for Equation with Real Numbers
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Undergrad Is the power series convergent in the field of p-adic numbers?
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Can a Matrix with Only 1s and -1s Have a Determinant Divisible by 2^(n-1)?
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High School Smallest N for Ensuring 3 Colors in 100 Marble Draw
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Undergrad How Do You Solve the Integral from POTW #156?
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Is $e^{\pi}$ greater than $\pi^{e}$?
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High School Real Number Problem: Evaluate xyz with Given Equations
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Undergrad How to Prove the Decomposition Theorem for Projections on a Vector Space?
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How to Check if a Number is Prime in Python?
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High School Can You Solve the Equation with Logs: $\log_2 (\cos x)=2\log_3 (\cot x)$?
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Problem of the Week # 163 - May 12, 2015
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Undergrad Is the Convergence of a Real Number Series Determined by Positive Integers?
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High School What is the Range of x for $|x|^{x^2-3x-4}<1$?
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Undergrad Is Any Real Zero of This Polynomial Greater Than M+1?
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What is the direction of the velocity vector on the rising side of a cycloid?
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High School Find the $2015$th Term in Sequence $1,2,-2,3,-3,3,4,-4,4,-4,5,-5,5,-5,5\cdots$
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What is the height of the tennis ball after bouncing off a basketball?
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Undergrad What is the integral of cos(x^3)?
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High School How to Evaluate Trigonometric Cosine Sums Manually?
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Undergrad How can you prove that a matrix is equal to zero if its trace is always zero?
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Undergrad How can you prove the linearity of a functional using a signed Borel measure?
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Problem of the Week # 160 - April 21, 2015
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High School Which values of $a$ satisfy a trigonometric equation in a given interval?
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High School Can You Prove This Inequality Involving Fractions and Square Roots?
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Problem of the Week # 159 - April 14, 2015
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Is this Roulette Wheel Fair? Statistical Analysis and Casino Manager's Claim
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Undergrad Is the Alternating Sum of Dimensions in an Exact Sequence Zero?
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High School Prove $X\ge 0$ and Find Smallest Positive $X$ | POTW #158 April 8, 2015
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What Was the Function g in This Week's Differentiation Problem?
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Undergrad Equinumerous partitions into distinct parts from X and Y?
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High School What Is the Maximum Value of P(x) in the Sequence?
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What is the Improved Solution for a Non-Small Angle Simple Pendulum?
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Undergrad Can a left Noetherian ring have $xy = 1$ without also having $yx = 1$?
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High School Finding the Least Possible Value of $a$ for a Perfectly Balanced School Club
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Can the closed unit interval be divided into smaller intervals?
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What is the Integral of e to the Maximum Power?
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High School How many digits are after the decimal in $\dfrac{12345678910}{2^{36}\cdot 5^6}$?
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High School How Can You Prove BC^2 Equals BK Times BQ in Equilateral Triangles?
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Undergrad How can I prove that $A_1$ is conformally equivalent to $A_2$?
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Problem of the Week # 154 - March 9, 2015
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