Math Problem of the Week Forum

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Undergrad How can we construct a chain homotopy between homotopic chain maps?
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High School What Is the Exact Value of the Real Root in the Equation \(x^3 + 3x - 2 = 0\)?
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Can You Solve the 1999 Putnam Competition Problem A-5?
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Undergrad Is $\mathcal{M}(X)$ a Banach space?
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High School What is the Value of x in the Equation $\sqrt{x^3+1648}-\sqrt{4949-x^3}=75$?
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High School How Can You Maximize This Square Root Expression for All Real Numbers?
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Undergrad Is a finite group of homeomorphisms with no fixed points able to act properly discontinuously on a Hausdorff space?
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What is the solution to Problem A-4 in the 1999 Putnam Mathematical Competition?
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Can you prove the power series expansion for (1-2x-x^2) has a specific pattern?
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High School What Is the Value of a+b If (a+√(a²+1))(b+√(b²+1))=1?
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Can a nonnegative polynomial be expressed as a sum of squares of polynomials?
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Undergrad Is an analytic map with a certain condition injective?
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High School Find the Value of a Polynomial with Given Constraints - POTW #250 Jan 17th, 2017
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High School What Is the Winning Probability for Player One in an N-Sided Die Game?
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How to Find Polynomials for a Piecewise Function?
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Problem of the Week # 247 - Jan 02, 2017
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Undergrad Can a homeomorphism of the closed unit disk map $S^1$ onto $S^1$?
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High School Can You Prove the Inequality in This Week's Math Challenge?
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Undergrad Can Uniformly Bounded Functions Converge Weakly to Zero in $\mathscr{L}^p$?
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What Are the Conditions for This Putnam Problem's Sum to Equal Zero?
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High School What is the decimal part of the sixth power of the sum of two square roots?
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Undergrad How can you prove that a retract of a Hausdorff space is always closed?
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What is the minimum perimeter of a triangle with given vertices?
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High School Can You Solve This Week's Math Challenge Equation?
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Undergrad Can the center of a finite group determine the size of its conjugacy classes?
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High School Problem of the week #245 Dec 14th, 2016
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What is the minimum value of a complex expression?
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High School Probability of |x-y|>=6 for Two Numbers in Range [0,10]
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Undergrad Can an Entire Function Be Non-Zero with Finite Double Integral?
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Can three points form a square?
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Undergrad Why is $M/(N\cap P)$ Artinian when $M/N$ and $M/P$ are Artinian?
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High School What Are the Last Two Digits of the Sum of Factorials from 7! to 2016!?
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What is the expected length of the shorter segment when the stick snaps?
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Undergrad What is the Homological Degree of a Fixed Point Free Continuous Map?
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High School Can You Find a Function That Satisfies This Integral Equation?
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Can a finite collection of open discs cover a given set in two dimensions?
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Undergrad Is $\omega^2$ nowhere vanishing on the four-sphere?
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High School Can You Solve This Complex Quadratic Expression by Hand?
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What are the solutions to Problem of the Week #240 - Nov 07, 2016?
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Undergrad Is every $S^{-1}R$-module flat?
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High School Can xyz Exceed 1 Given x^2 + y^2 + z^2 + xyz = 4?
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Undergrad How to Prove Convergence in Sequence $(x_n)_{n=1}^\infty$?
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Problem of the Week # 239 - Oct 28, 2016
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High School What Are the Solutions for the Exponential Equation \( x^{(y^z)} = (x^y)^z \)?
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Undergrad How Do You Prove the Boundedness of an Integral Operator in Measure Spaces?
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High School Can You Solve the Triangle $PQR$ Equation from POTW #238?
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Problem of the Week # 238 - Oct 20, 2016
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Undergrad Can an invertible sheaf be isomorphic to the structure sheaf?
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High School Can You Solve the Trigonometry Puzzle of the Week?
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How can a cube be inscribed in a right circular cone?
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Undergrad Is This Week's Math Problem of the Week Still Unsolved?
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What is the solution to Problem B-5 in the 1997 Putnam Competition?
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Undergrad Is the Quotient Sheaf Isomorphic to the Image Sheaf?
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High School What is the solution to evaluating this fraction series?
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What is the maximum sum of coefficients in a binomial expansion?
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High School How to Minimize the Sum of Squares with Given Distinct Elements?
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Undergrad How to solve Problem of the Week #226?
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What is the sum of a positive integer in fraction form?
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Undergrad Problem of the Week #225 - Sep 20, 2016
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High School Can You Solve the Trigonometric Equation for \(\tan^2 9^\circ\)?
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Problem of the Week # 233 - Sep 15, 2016
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Undergrad Is the mapping from $\mathcal{L}^p(X,\mu)$ to $\mathcal{L}^1(X,\mu)$ continuous?
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High School How Many Ways to Fit Six People in Four Rooms?
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What is the solution to Problem A-6 in the 1997 Putnam Mathematical Competition?
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High School Find the Ratio of BG to FG in a Figure with Given Side Lengths
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Undergrad Why must $G$ be the internal direct product of $H$ and $K$?
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What is the area of region $S$?
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Undergrad How Do You Solve the Integral in POTW #222?
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High School How Do You Solve the Integral Challenge from POTW #231?
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Is $N_{10}$ even or odd?
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High School Solution for POTW #230: Calculate g^(3)(0) for f(x)
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Undergrad Can Every Smooth Map from a Manifold to the Complex Numbers be Lifted to the Exponential Map?
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Can a Group Have Multiple Homomorphisms With the Same Identity?
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Undergrad Can a Function Belong to L^1 and have a Maximal Function in L^1?
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High School Can You Solve the Cube of Cosines for Specific Angles?
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Can You Solve the Origin-Inclusion Convex Polygon Problem?
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High School Can You Solve This Challenging Inequality Involving Real Numbers?
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Undergrad Can Nonsingular Matrices Be Generated by Multiplying and Adding?
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Is there a 2x2 matrix with real entries whose sine is [1, 2016; 0, 1]?
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Undergrad Can an entire function with exponential growth have bounded derivatives?
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High School Is Sin 1 Less Than Log Base 3 of Root 7?
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What is the maximum sum of products of consecutive integers from 1 to n?
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Undergrad How Does the Limit of the Integral Relate to the Sinc Integral?
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High School Proving the Non-Perfect Square Property of 4 Consecutive Positive Integers
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Can you prove the inequality for positive integers?
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Undergrad What is the sum of quadratic residues in $\Bbb Z/p\Bbb Z$ for a prime $p > 3$?
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High School How Can You Rewrite x²/(x⁴+x²+1) Using u?
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Why Is the Sum of Certain Binomial Coefficients Divisible by \( p^2 \)?
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High School Triangle Inequality Proof: Shortest Side in Relation to Sides a, b, and c
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Undergrad Can a Function Be Discontinuous Only at Irrationals?
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How Can You Prove the Existence of a Function in POTW #223?
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Undergrad What is a non-trivial unit in the integral group ring Z[S_3]?
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High School What are the positive integers for which $n^8+n^4+1$ is prime?
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Undergrad Is every polynomial a unit in a commutative ring with unity?
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Problem of the Week # 222 - Jun 29, 2016
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High School How Can You Express Cos(a-b) in Terms of m and n?
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Problem of the Week # 221 - Jun 21, 2016
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Undergrad Can You Solve This Infinite Series Challenge?
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High School Solution from greg1313:Solution from lfdahl:
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Problem of the Week # 220 - Jun 14, 2016
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