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combinatorics

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Model Perspective
Model Perspective
Nov 15, 2024 · Fundamentals

Unlocking Mathematical Thinking: Proofs, Sets, Functions, and Infinity Explained

This article explores core mathematical thinking—from induction proofs and set theory to bijective functions, combinatorial counting, and Cantor’s proof of uncountable reals—illustrating how rigorous logic and abstract concepts provide clear solutions to complex problems across various contexts.

Infinitycombinatoricsmathematics
0 likes · 8 min read
Unlocking Mathematical Thinking: Proofs, Sets, Functions, and Infinity Explained
Model Perspective
Model Perspective
Oct 26, 2022 · Fundamentals

How Mathematical Modeling Turns Complex Problems into Simple Proofs

This article shows how adopting appropriate mathematical models—function, geometric, combinatorial, and similarity models—can transform intricate algebraic and geometric proof problems into clear, concise solutions, illustrating each approach with concrete examples and visual aids.

algebracombinatoricsgeometry
0 likes · 6 min read
How Mathematical Modeling Turns Complex Problems into Simple Proofs
Python Programming Learning Circle
Python Programming Learning Circle
Apr 9, 2022 · Fundamentals

Algorithmic Solutions for Seven Programming Problems (Number Cards, Grid Lines, Cube Packing, Shortest Path, Hamiltonian Cycle, Time Display, Pascal's Triangle)

This article presents detailed problem statements, mathematical analysis, and Python implementations for seven algorithmic challenges covering combinatorial counting, geometry, number theory, graph shortest paths, Hamiltonian cycles, time conversion, and Pascal's triangle indexing.

Algorithmcombinatoricscompetitive programming
0 likes · 14 min read
Algorithmic Solutions for Seven Programming Problems (Number Cards, Grid Lines, Cube Packing, Shortest Path, Hamiltonian Cycle, Time Display, Pascal's Triangle)
IT Services Circle
IT Services Circle
Mar 14, 2022 · Fundamentals

Counting Isosceles Acute Triangles in a Regular n‑gon – Analysis and Java Solution

This article explains how to count the number of isosceles acute‑angled triangles whose vertices lie on the vertices of a regular n‑gon, discusses separate cases for even and odd n, handles duplicate equilateral triangles, and provides a correct Java implementation that avoids integer overflow.

AlgorithmJavaLeetCode
0 likes · 8 min read
Counting Isosceles Acute Triangles in a Regular n‑gon – Analysis and Java Solution
IT Services Circle
IT Services Circle
Mar 7, 2022 · Fundamentals

Counting Isosceles Acute Triangles in a Regular n‑gon – Analysis and Java Solution

This article explains how to count the number of isosceles acute triangles whose vertices lie on a regular n‑gon (3 ≤ n ≤ 10⁷), derives separate formulas for even and odd n, handles duplicate equilateral cases, and provides a correct Java implementation that avoids overflow.

AlgorithmJavacoding
0 likes · 8 min read
Counting Isosceles Acute Triangles in a Regular n‑gon – Analysis and Java Solution
Full-Stack Internet Architecture
Full-Stack Internet Architecture
May 20, 2021 · Fundamentals

Understanding Full Permutations and Backtracking in Java

This article explains the concept of full permutations, presents a classic interview problem requiring all permutations of a distinct integer array, and walks through a backtracking solution in Java with detailed step‑by‑step analysis and code examples.

AlgorithmDFSJava
0 likes · 6 min read
Understanding Full Permutations and Backtracking in Java
Python Programming Learning Circle
Python Programming Learning Circle
Apr 20, 2020 · Fundamentals

Understanding Binomial Distribution, Permutations, Combinations, and Their Python Implementations

This article introduces the fundamentals of binomial and Bernoulli distributions, explains permutations and combinations, provides Python functions to compute them, demonstrates probability calculations and visualizations with matplotlib and plotly, and shows a maximum likelihood estimation example for binomial parameters.

MLEbinomial distributioncombinatorics
0 likes · 8 min read
Understanding Binomial Distribution, Permutations, Combinations, and Their Python Implementations
Python Programming Learning Circle
Python Programming Learning Circle
Jan 14, 2020 · Fundamentals

Generate All Unique 3‑Digit Numbers and Compute Tiered Bonuses with Python

This article demonstrates two Python programming exercises: generating all unique three‑digit numbers from digits 1‑4 using nested loops, and calculating a tiered profit‑based bonus by segmenting profit ranges, complete with source code, analysis, and sample outputs.

Algorithmbeginner programmingbonus calculation
0 likes · 4 min read
Generate All Unique 3‑Digit Numbers and Compute Tiered Bonuses with Python
Architects Research Society
Architects Research Society
Oct 30, 2016 · Fundamentals

Why Some Areas of Mathematics Feel Harder Than Others

The perceived difficulty of mathematical fields varies because each branch has its own language, foundational concepts, and required tools, making areas like algebraic geometry seem daunting while others such as number theory or combinatorics appear simpler yet still demand deep insight and advanced techniques.

PDEalgebraic geometrycombinatorics
0 likes · 8 min read
Why Some Areas of Mathematics Feel Harder Than Others