Math Problem of the Week Forum

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What Are the Dimensions of the Largest Box Inscribed in a Tetrahedron?
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McDonald's Chicken McNugget Combo Conundrum: Week #53
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Which isosceles triangle with a given perimeter has the greatest area?
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How can contour integration be used to solve this week's problem?
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Where was the cue ball struck to initiate rolling without slipping?
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Can you prove the identity using calculus?
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Is the SL(2,R) action on the upper half-plane transitive?
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What is $a+b+c$ for \( f(x+3)=3x^2+7x+4 \) and \( f(x)=ax^2+bx+c \)?
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Can You Tackle This Week's Fourier Series Challenge?
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Can you solve the Problem of the Week #41 - March 11th, 2013?
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Imaginary Number Problem: Finding the Sum of Powers of i - March 12, 2012
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What is the Galois group and splitting field for the polynomial $x^3-3x+1$?
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Is H an abelian group of order 9 and is it isomorphic to Z9 or Z3 x Z3?
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What is the smallest value of n that assures at least a 50% chance that at least two students select the same integer?
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Problem of the Week #48 - February 25th, 2013
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Can You Solve This Week's Complex Analysis Problem?
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Prove \cos Formulas: \frac{\pi}{7}, \frac{2\pi}{7}, \frac{3\pi}{7} & General Sum
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Problem of the Week #47 - February 18th, 2013
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Is a Finite-Dimensional Module with Distinct Diagonal Entries Cyclic?
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Problem #47: Finding Masses for Center of Mass at Origin - February 18, 2013
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A transition probability matrix $\mathbf{P}$ is said to be doubly stochastic if the sum over each column equals one
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How Long Will the Rat Be Trapped in the Maze?
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This value is constant for any arbitrary point $(x_0,y_0)$ on either hyperbola.
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What is the smallest integer that satisfies $29 \mid n^2 - 5$?
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Is $\textrm{GL}_2(\mathbb{Z}/2\mathbb{Z})$ Isomorphic to $\text{Sym}(3)$?
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What is the ratio of Adam and his son's ages 6 years later?
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Why is Green's theorem for circular boundaries a consequence of Stoke's theorem?
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How can we use integration by parts to prove the formula for $J_{n+1}$?
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Counting Routes in a 4x6 Grid: How Many Ways to Reach the End?
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Where is the Gaussian curvature zero, maximum, and minimum on a torus?
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How Does the Limit of the Sum Approach One Half in POTW #43?
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Calculating P(A ∪ B) - P(A ∩ B) with Given Probabilities
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Solving System of Equations Using Cramer's Rule - Problem #42 | Jan 14th, 2013
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Can You Find the Minimal and Characteristic Polynomials of This Operator?
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Can You Master This Week's Challenge on Laplace Transforms and Convolution?
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How can we simplify the triple integral of a rectangular box?
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Is $A^4=1$ for a $3\times 3$ matrix over $\mathbb{Q}$ if $A^8=1$?
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Choosing $5,000,000 or 1 Penny a Day: Which is More Profitable? | Problem #41
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Is the integral of a nonnegative Lebesgue integrable function continuous?
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What is the probability identity for multiple events?
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Find Roots of 2x^4+11x^3-24x^2-19x+14 Without Calculator | Problem #40
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Can $f(iA)$ be a unitary operator if $A$ is hermitian?
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Can we prove this using the Binet's formula for the Fibonacci sequence?
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HAPPY HOLIDAYS Arrangements and Fraction Calculation
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What is the flow of a vector field with a constant vector and linear map?
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Can you find a continuous solution to this differential equation?
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How much time elapsed between two clock observations?
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Can You Solve the Hamilton-Jacobi Equation for the Linear Harmonic Oscillator?
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How to Apply the Gram-Schmidt Process to Obtain an Orthonormal Basis for $P_2$?
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Volume Equivalence Condition for Revolving Parabolas
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Week #36 - Simplifying Trigonometric Expressions | December 3rd, 2012
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How do we prove the convergence of a series involving non-integral values?
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How can you calculate the area of a polygon given its vertices?
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How can you prove that $n^{13}-n$ is divisible by $2730$ for all $n$?
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How do you solve the integral of 1 over (a+cos(theta)^2) from 0 to 2pi for a>1?
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Train Collision Bird Flight Problem - Week 35 (11/26/2012)
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What is the relationship between derivations and automorphisms of a Lie algebra?
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Can you solve this week's production cost optimization problem?
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Problem of the week #34 - November, 19th 2012
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Is $H$ a characteristic subgroup of $G$ when $G$ is abelian?
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What is the pre-image of a group homomorphism?
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Problem of the week #33 - November 12th, 2012
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Problem of the Week #23 - November 5th, 2012
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Problem of the Week #32 - November 5th, 2012
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When is this man's birthday?
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Is Compactness Equivalent to Limit Point Compactness in Topological Spaces?
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What is the residue of a complex valued function at a pole of order $m$?
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Therefore, the special four-digit number is 9376.
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What is the solution to Problem of the Week #21?
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How do we show that $L$ is diagonalizable?
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Now, can you prove this limit using the Limit Definition of Continuity
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Are polar coordinates $r$ and $\theta$ harmonic in terms of $x$ and $y$?
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What is the Laplacian of $y^k$ in the upper half plane with hyperbolic metric?
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Revolution Count for Two Wheels with Different Diameters
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Is the Inner Product of Matrices Preserved under Vector Multiplication?
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Can the Volterra operator have nonzero eigenvalues?
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What Could Be the Average Salary for All Employees in the Company?
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Problem of the Week #18 - October 1st, 2012
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Problem of the Week #27 - October 1st, 2012
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Mixing Alcohol Solutions: Calculating the Percentage of a New Solution
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What is the solution to this week's polynomial problem on the unit circle?
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What is the characteristic polynomial of a $2\times 2$ matrix?
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Triangle Area Problem: Which Side Lengths Yield Possible Areas?
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Is $F=(f_1,f_2) : N\rightarrow M_1\times M_2$ a smooth map?
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How can we use the $PA=LU$ decomposition to solve a system of linear equations?
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Calculating Probability of Getting Two Aces in Texas Hold Em
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What are the fundamental forms and curvatures of a helicoid in $\mathbb{R}^3$?
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Is $HK$ a subgroup of $G$ if and only if $HK=KH$?
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What is the inverse of $f$ for the Lorentz factor in special relativity?
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How many different ways can you group these letters into groups of 4, 4 and 6?
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Is the intersection of subgroups of G always a subgroup?
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Is the Uniform Limit of Continuous Functions on a Subset also Continuous?
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What is the total amount of rice taken to the market by three farmers?
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Is the product space Hausdorff if both $X$ and $Y$ are Hausdorff?
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Generalizing the Complex Number Formula for $(1+2i)^n$
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Calculating the Best Bet: Solving the Problem of Roulette Odds
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Is the Pre-image of a Borel Set Measurable?
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How do you construct a field with 27 elements?
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Is Continuity Preserved Under Union of Subspaces?
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How to show that $G(s) = \dfrac{F(s)}{s}$ for Laplace transforms of integrals?
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