PROBLEMS IN MATHEMATICS Archives

Understanding Ordered Pairs: Definition Examples and Applications

Learn the definition of an ordered pair in mathematics including its key characteristics and applications. Explore examples and understand how it’s used.

Solving Polynomial Equations: Finding q(uv) = 0

Discover how to solve polynomial equations and find q(uv) = 0. Learn techniques for determining polynomial relationships between variables. Polynomial Equation Solver.

Polynomial Matrix Decomposition: A Step-by-Step Guide

Learn how to decompose polynomial matrices using elementary row operations. This guide provides a step-by-step approach to polynomial matrix decomposition.

Understanding Inequalities in Harmonic Homogeneous Polynomials

Explore the inequality concerning the dimension of harmonic homogeneous polynomials. Learn about the relationship between homogeneous polynomials and their Laplacian. Harmonic Homogeneous Polynomials explained.

Polynomial Ratio Image: Exploring the Image of a Ratio of Polynomials in ℂ

Investigating the image of a ratio of polynomials with affine coefficients. Does the image lie within a complex polytope defined by vertices? Polynomial Ratio Image.

Chebyshev Polynomials Series: Exploring Patterns in Polynomial Coefficients

Discover the fascinating relationship between Chebyshev polynomials of the second kind and binomial coefficients in this exploration of series. Chebyshev Polynomials Series.

Non-commutative Product Expansion: Rewriting Products as Sums

Learn how to rewrite a non-commutative product as a sum. This guide explores methods for expanding products of non-commuting elements offering both general formulas and recursive approaches. Non-commutative Product Expansion explained.

Computing the Ideal of a Projective Algebraic Set in P^2(C)

Learn how to compute the ideal of a projective algebraic set in P^2(C). This post explores methods for determining the ideal including geometric approaches and Gröbner bases. Projective Algebraic Set Ideal.

Calculating the Change of Basis Matrix for Linear Maps on Polynomials

Learn how to calculate the change of basis matrix for linear maps on polynomials. This guide clarifies common discrepancies and misunderstandings. Change of Basis Matrix explained.

What is Coulomb’s Law and How Did Coulomb Discover It?

Learn about Coulomb’s Law the inverse square law of force and how French physicist Charles-Augustin de Coulomb discovered it.

Understanding Open and Closed Intervals: Definitions and Examples

Learn about open and closed intervals in mathematics including definitions and examples. Essential for understanding calculus.

Understanding Sequences and Limits: A Comprehensive Guide

Learn about sequences their limits and how they differ from functions. Discover convergence and divergence and essential theorems.

Understanding Open and Closed Intervals in Mathematics

Learn about open and closed intervals in mathematics including definitions and examples using mathjax notation.

Can Subsets of Natural Numbers Have Equal Harmonic Series Sums?

Explore if disjoint subsets of natural numbers exist where the sum of harmonic series terms over each subset is equal. Investigate the harmonic series and its subset sums.

Can Natural Numbers Be Partitioned by Equal Digit Sum?

Can natural numbers be divided into two sets with equal sums of their digits? Explore this intriguing partitioning problem.

Finding Subsets of Natural Numbers with Equal Sums of Reciprocals of Squares

Discover how to find subsets of natural numbers where the sum of reciprocals of their squares is equal exploring both finite and infinite cases.

Understanding L'Hôpital's Rule for Limits: A Comprehensive Guide

Learn how L'Hôpital's rule helps evaluate indeterminate forms in limits. This guide provides a complete explanation and examples.

Understanding Quadratic Polynomial Zeroes: Example and Explanation

Discover the zeroes of the quadratic polynomial passing through specific points.

Determining Inequality Coefficients for Positive Real Numbers

Explore the inequality coefficients problem for positive real numbers and find possible permutations.

Solving the Distinct Real Numbers Problem with Equations

Explore the solutions for distinct real numbers satisfying specific equations in this insightful blog post.

Calculating Distance in 3D: Understanding Triangular Relationships

Learn how to calculate distance in 3D using triangular relationships and trigonometric ratios.

How to Find the Remainder of Polynomial Division

Learn how to find the remainder of polynomial division using standard and alternate methods.

Understanding Sophie Germain Primes: Properties Applications and Algorithms

Discover Sophie Germain primes special prime numbers with unique properties. Learn about their relation to safe primes applications in cryptography and how to identify them using Python.

Solving the Surjective Function Equation f(x) for Positive Real Numbers

Discover the surjective functions f(x) that satisfy the equation 2xf(f(x)) = f(x)(x + f(f(x))) for all positive real numbers x.

Solving Functional Equations: Finding f(x) and g(x)

Discover how to find functions f(x) and g(x) that satisfy a specific functional equation. Explore different cases and solutions.

Solving Surjective Functions: A Functional Equation Approach

Discover how to find all surjective functions f:R→R satisfying a specific functional equation. Learn the key steps and techniques.

Solving Functional Equations: Tips and Tricks for Midterm Prep

Struggling with functional equations for your math midterm? This post provides tips and tricks including substituting values using mathematical induction and finding fixed points to help you solve these challenging problems.

Understanding Vectors in Mathematics: Definition Operations and Applications

Learn about vectors in mathematics their properties and how they’re used in physics computer graphics and machine learning.

Proving Mathematical Propositions: Direct Indirect and Other Methods

Learn various methods for proving mathematical statements including direct proof indirect proof (contradiction and contrapositive) proof by cases and mathematical induction. Explore examples and applications.