math-games.qmd

---
title: "Custom Math (Board/Party) Games"
description-meta: "Derek Wang custom math games"
page-layout: full
back-to-top-navigation: true
toc: true
toc-location: right
css:
  - styles.css
  - math-games.css
---

Here I've compiled some math-themed versions of board/party games. I only provide the "cards" or equivalent textual components of each game.
You probably need a physical set to actually play these. 

## 5 Second Rule

```{=html}
<div id="fsr-container" class="fsr-container">
  <div id="fsr-menu" class="fsr-menu"></div>
  <div id="fsr-content" class="fsr-content">
    <div id="fsr-cards" class="fsr-cards"></div>
  </div>
</div>

<script>

let currentTheme = null;
let currentIndex = 0;

const fsrThemes = {
  'General': [
    { front: 'Name <strong>3</strong> branches of mathematics categorized as <strong>algebra</strong>', back: '<strong>Sample Responses:</strong> algebraic topology, algebraic geometry, algebraic number theory' },
    { front: 'Name <strong>3</strong> branches of mathematics categorized as <strong>analysis</strong>', back: '<strong>Sample Responses:</strong> real analysis, complex analysis, functional analysis, stochastic analysis' },
    { front: 'Name <strong>3</strong> branches of <strong>applied mathematics</strong>', back: '<strong>Sample Responses:</strong> mathematical biology, mathematical physics, scientific computing, algorithms' },
    { front: 'Name <strong>3 transforms</strong> of any kind', back: '<strong>Sample Responses:</strong> Legendre, Fourier, Laplace' },
    { front: 'Name <strong>3</strong> objects one may refer to as <strong>conjugate</strong> in any sense', back: '<strong>Sample Responses:</strong> conjugate variables, roots of polynomials, complex conjugates, conjugate matrices, conjugate transpose' },
    { front: 'Name <strong>3 spaces</strong> of any kind', back: '<strong>Sample Responses:</strong> vector space, metric space, inner product space, Hilbert space, Banach space, tangent space, phase space' },
    { front: 'Name <strong>3</strong> objects one may refer to as <strong>normal</strong> in any sense', back: '<strong>Sample Responses:</strong> matrices, subgroups, orthogonal lines, modes' },
    { front: 'Name <strong>3</strong> properties any function might have', back: '<strong>Sample Responses:</strong> injectivity, surjectivity, bijectivity' },
    { front: 'Name <strong>3 inequalities</strong> of any kind', back: '<strong>Sample Responses:</strong> AM-GM, Cauchy-Schwarz inequality, triangle inequality, Markov\'s inequality' },
    { front: 'Name <strong>3</strong> things that begin with <strong>eigen-</strong>', back: '<strong>Sample Responses:</strong> eigenvector, eigenvalue, eigenspace, eigenfunction, eigenmodes' },
    { front: 'Name <strong>3</strong> ways to use a lower-case <strong>delta</strong> symbol', back: '<strong>Sample Responses:</strong> Kronecker delta, Dirac delta, a small angle, variation of a functional' },
    { front: 'Name <strong>3</strong> famous <strong>constants</strong> in mathematics', back: '<strong>Sample Responses:</strong> Golden Ratio, e, pi' },
    { front: 'Name <strong>3</strong> <strong>trigonometric</strong> functions', back: '<strong>Sample Responses:</strong> sine, cosine, tangent' },
    { front: 'Name <strong>3</strong> ways to solve a <strong>quadratic equation</strong> with real coefficients', back: '<strong>Sample Responses:</strong> factoring, quadratic formula, completing the square, polynomial division' },
    { front: 'Name <strong>3</strong> types (in some sense) of <strong>proofs</strong>', back: '<strong>Sample Responses:</strong> by construction, by contradiction, by induction' },
  ],

  'People': [
    { front: 'Name <strong>3</strong> mathematicians considered to be important figures in <strong>algebra</strong>', back: '<strong>Sample Responses:</strong> Galois, Abel, Noether, Lagrange, Gauss' },
    { front: 'Name <strong>3</strong> mathematicians considered to be important figures in <strong>analysis</strong>', back: '<strong>Sample Responses:</strong> Cauchy, Weierstrass, Riemann, Lebesgue, Leibniz, Hilbert, Banach' },
    { front: 'Name <strong>3</strong> mathematicians considered to be important figures in <strong>geometry</strong>', back: '<strong>Sample Responses:</strong> Euclid, Riemann, Poincare, Minkowski' },
    { front: 'Name <strong>3</strong> things named after <strong>Euler</strong>', back: '<strong>Sample Responses:</strong> Euler\'s identity, Euler-Lagrange equations, Eulerian circuit, Euler angles, Euler\'s equations' },
    { front: 'Name <strong>3</strong> things named after <strong>Gauss</strong>', back: '<strong>Sample Responses:</strong> Gauss\' law, Gaussian distribution, Gaussian integers, Gaussian elimination' },
    { front: 'Name <strong>3</strong> things named after <strong>Cauchy</strong>', back: '<strong>Sample Responses:</strong> Cauchy sequence, Cauchy-Euler ODE, Cauchy-Schwarz inequality, Cauchy\'s Theorem, Cauchy completeness' },
    { front: 'Name <strong>3</strong> things named after <strong>2 or more</strong> mathematicians', back: '<strong>Sample Responses:</strong> Cauchy-Schwarz inequality, Euler-Lagrange equations, Heine-Borel Theorem, Bolzano-Weierstrass Theorem, Riemann-Stieltjes integral, Fokker-Planck equation, Hamilton-Jacobi-Bellman equation, Calderbank-Shor-Steane codes' },
    { front: 'Name <strong>3 contemporary</strong> mathematicians (past 50 years)', back: '<strong>Sample Responses:</strong> Tao , Mirzakhani, Daubechies, Wiles, Perelman' },
    { front: 'Name <strong>3 ancient</strong> mathematicians (before roughly 1000 CE)', back: '<strong>Sample Responses:</strong> Archimedes, Euclid, Diophantus, al-Khwarizmi' },
    { front: 'Name <strong>3 female</strong> mathematicians', back: '<strong>Sample Responses:</strong> Noether, Daubechies, Mirzakhani, Lovelace, Grace Hopper' },
    { front: 'Name <strong>3</strong> mathematicians with notable contributions in <strong>computer science</strong>', back: '<strong>Sample Responses:</strong> Turing, Shannon, Lovelace, Shor, Calderbank' },
    { front: 'Name <strong>3</strong> mathematicians with notable contributions in <strong>mathematical finance</strong>', back: '<strong>Sample Responses:</strong> Black and Scholes, Jim Simons' },
    { front: 'Name <strong>3</strong> mathematicians with notable contributions in <strong>mathematical physics</strong>', back: '<strong>Sample Responses:</strong> Gauss, Euler, Lagrange, Laplace, von Neumann, Noether, Hilbert, Weyl' },

  ],

  'Calculus': [
    { front: 'Name <strong>3</strong> theorems from <strong>vector calculus</strong>', back: '<strong>Sample Responses:</strong> Stokes\' Theorem, Green\'s Theorem, Divergence Theorem' },
    { front: 'Name <strong>3</strong> ways to <strong>differentiate</strong> a function in any sense', back: '<strong>Sample Responses:</strong> gradient, curl, divergence' },
    { front: 'Name <strong>3</strong> "rules" of <strong>differentiation</strong>', back: '<strong>Sample Responses:</strong> power rule, product rule, chain rule, quotient rule, l\'Hopital\'s rule, Leibniz rule' },
    { front: 'Name <strong>3 integration</strong> techniques', back: '<strong>Sample Responses:</strong> integration by parts, partial fractions, Leibniz rule' },
    { front: 'Name <strong>3</strong> types of <strong>vector integrals</strong>', back: '<strong>Sample Responses:</strong> line integral, path integral, surface integral' },
    { front: 'Name <strong>3</strong> coordinate systems for <strong>Euclidean 3-space</strong>', back: '<strong>Sample Responses:</strong> Cartesian, cylindrical or polar, spherical' },
    { front: 'Name <strong>3</strong> types of <strong>discontinuities</strong>', back: '<strong>Sample Responses:</strong> jump, cusp, corner' },

  ],

  'Linear Algebra': [
    { front: 'Name <strong>3</strong> ways to <strong>decompose</strong> a matrix', back: '<strong>Sample Responses:</strong> LU, QR, SVD' },
    { front: 'Name <strong>3</strong> ways to characterize a <strong>matrix</strong>', back: '<strong>Sample Responses:</strong> invertible, upper triangular, symmetric, orthogonal, Hermitian, unitary' },
    { front: 'Name <strong>3</strong> canonical <strong>matrix forms</strong>', back: '<strong>Sample Responses:</strong> row reduced echelon form, Smith normal form, Hermite normal form' },
    { front: 'Name <strong>3</strong> ways to conclude a square matrix is <strong>invertible</strong>', back: '<strong>Sample Responses:</strong> full rank, trivial null space, column space = codomain' },
    { front: 'Name <strong>3 vector space axioms</strong>', back: '<strong>Sample Responses:</strong> additive identity, additive inverse, closure under vector addition, closure under scalar multiplication' },
    { front: 'Name <strong>3</strong> theorems associated with linear algebra', back: '<strong>Sample Responses:</strong> Spectral Theorem, Rank-Nullity, Cayley-Hamilton' },
    { front: 'Name <strong>3</strong> ways to solve a linear <strong>system of equations</strong>', back: '<strong>Sample Responses:</strong> Gaussian elimination or row reduction, Cramer\'s Rule, matrix inversion' },
    { front: 'Name <strong>3</strong> applications of <strong>eigenvectors</strong>', back: '<strong>Sample Responses:</strong> solving linear systems of ODEs, analyzing finite-state Markov chains, computing normal mode frequencies' },
  ],

  'Differential Eqns': [
    { front: 'Name <strong>3</strong> ways to solve an <strong>inhomogeneous ODE</strong>', back: '<strong>Sample Responses:</strong> integrating factor, undetermined coefficients, variation of parameters' },
    { front: 'Name <strong>3</strong> types of <strong>equilibrium points</strong> for a linear autonomous system', back: '<strong>Sample Responses:</strong> nodal source/sink, spiral source/sink, saddle' },
    { front: 'Name <strong>3</strong> standard <strong>PDEs</strong>', back: '<strong>Sample Responses:</strong> heat equation, wave equation, Hamilton-Jacobi equation, Fokker-Planck equation' },
    { front: 'Name <strong>3</strong> types of <strong>boundary conditions</strong> for ODEs', back: '<strong>Sample Responses:</strong> Dirichlet, Neumann, Robin' },
  ],
  
  'Probability/Stats/ML': [
    { front: 'Name <strong>3</strong> probability distributions', back: '<strong>Sample Responses:</strong> Gaussian, Bernoulli, binomial, geometric, Poisson, uniform' },
    { front: 'Name <strong>3</strong> ways for a <strong>random variable</strong> to converge', back: '<strong>Sample Responses:</strong> in distribution, in probability, almost surely' },
    { front: 'Name <strong>3</strong> distributions in the <strong>exponential family</strong>', back: '<strong>Sample Responses:</strong> Gaussian, Bernoulli, binomial, Poisson, exponential, gamma, Dirichlet' },
    { front: 'Name <strong>3</strong> tests for <strong>statistical significance</strong>', back: '<strong>Sample Responses:</strong> z-test, t-test, f-test, likelihood ratio test' },
    { front: 'Name <strong>3</strong> theorems associated with probability', back: '<strong>Sample Responses:</strong> Weak and Strong Laws of Large Numbers, Central Limit Theorem, Bayes\' Rule, Radon-Nikodym Theorem' },
    { front: 'Name <strong>3 inequalities</strong> in probability', back: '<strong>Sample Responses:</strong> Jensen\'s inequality, Markov\'s inequality, Chebyshev\'s inequality' },
    { front: 'Name <strong>3 optimization algorithms</strong>', back: '<strong>Sample Responses:</strong> gradient descent, stochastic gradient descent, proximal gradient descent' },
    { front: 'Name <strong>3 dimension reduction</strong> methods', back: '<strong>Sample Responses:</strong> PCA, MDS, Isomap, tSNE' },
    { front: 'Name <strong>3 MCMC sampling</strong> methods', back: '<strong>Sample Responses:</strong> Gibbs, Metropolis-Hastings, Langevin dynamics' },
    { front: 'Name <strong>3</strong> stochastic processes which are characterized as <strong>Markovian</strong>', back: '<strong>Sample Responses:</strong> random walks, Brownian motion, Poisson process, Langevin dynamics' },
    { front: 'Name <strong>3</strong> ways to assess a <strong>statistical model</strong>', back: '<strong>Sample Responses:</strong> R2, RMSE, AIC or BIC' },
    { front: 'Name <strong>3</strong> assumptions of generic <strong>linear models</strong>', back: '<strong>Sample Responses:</strong> underlying linear relationship, independence of errors, equal variance of errors' },
    { front: 'Name <strong>3</strong> standard machine learning <strong>architectures</strong>', back: '<strong>Sample Responses:</strong> CNN, transformer, U-Net, GAN, VAE' },
    { front: 'Name <strong>3 regularization</strong> techniques in machine learning', back: '<strong>Sample Responses:</strong> L2, L1 or LASSO, dropout, weight decay' },
  ],

  'Abstract Algebra': [
    { front: 'Name <strong>3 algebraic structures</strong>', back: '<strong>Sample Responses:</strong> group, ring, field, vector space' },
    { front: 'Name <strong>3</strong> ways to characterize a <strong>group</strong>', back: '<strong>Sample Responses:</strong> cyclic, permutation, dihedral, Abelian' },
    { front: 'Name <strong>3</strong> ways to characterize a <strong>ring</strong>', back: '<strong>Sample Responses:</strong> division ring, integral domain, prime factorization domain, principal ideal domain, Euclidean domain' },
    { front: 'Name <strong>3 platonic solids</strong>', back: '<strong>Sample Responses:</strong> tetrahedron, cube, octahedron, icosahedron, dodecahedron' },
    { front: 'Name <strong>3</strong> groups of <strong>order up to 10</strong>', back: '<strong>Sample Responses:</strong> cyclic groups of order 2 through 10, Klein-4 group, S3 or D3, D4' },
    { front: 'Name <strong>3</strong> groups of <strong>order greater than 10</strong>', back: '<strong>Sample Responses:</strong> cyclic groups of order more than 10, S4 and up, D6 and up, icosahedral group, Mathieu group, Monster group' },
    { front: 'Name <strong>3</strong> ways to characterize a <strong>subgroup</strong>', back: '<strong>Sample Responses:</strong> normal, center, centralizer, normalizer, stabilizer, commutator' },
    { front: 'Name <strong>3 group axioms</strong>', back: '<strong>Sample Responses:</strong> closure, identity, inverses, associativity' },
  ],

  'Real Analysis': [
    { front: 'Name <strong>3</strong> equivalent characterizations of the <strong>completeness</strong> of the <strong>reals</strong>', back: '<strong>Sample Responses:</strong> Bolzano-Weierstrass Theorem, Heine-Borel Theorem, least upper bound property, Cauchy completeness, Monotone Convergence Theorem, Nested Interval property' },
    { front: 'Name <strong>3</strong> properties from which <strong>Riemann integrability</strong> follows', back: '<strong>Sample Responses:</strong> continuity, monotonicity, finite set of discontinuities' },
    { front: 'Name <strong>3</strong> tests for the <strong>convergence</strong> of a <strong>numerical series</strong>', back: '<strong>Sample Responses:</strong> ratio test, root test, comparison test, integral test, Dirichlet test' },
    { front: 'Name <strong>3</strong> types of <strong>series</strong>', back: '<strong>Sample Responses:</strong> power series, Taylor series, Maclaurin series, Fourier series' },
    { front: 'Name <strong>3</strong> definitions that implicate an <strong>epsilon</strong> alongside a <strong>delta</strong> or <strong>N</strong>', back: '<strong>Sample Responses:</strong> limit of a sequence, Cauchy sequence, continuity' },
    { front: 'Name <strong>3</strong> theorems associated with <strong>differentiation</strong>', back: '<strong>Sample Responses:</strong> Fundamental Theorem of Calculus, Mean-Value Theorem, Taylor\'s Theorem' },
    { front: 'Name <strong>3</strong> properties enjoyed by the real numbers', back: '<strong>Sample Responses:</strong> least upper bound property, Archimedean property, completeness' },
    { front: 'Name <strong>3</strong> properties following from the <strong>continuity</strong> of a function on a <strong>compact</strong> domain', back: '<strong>Sample Responses:</strong> range is compact, function is uniformly continuous, function attains its extreme values' },
    { front: 'Name <strong>3</strong> properties of any <strong>metric</strong>', back: '<strong>Sample Responses:</strong> symmetry, positivity, triangle inequality' },
    { front: 'Name <strong>3</strong> terms that might precede the word <strong>"convergence"</strong> in any setting', back: '<strong>Sample Responses:</strong> absolute, monotone, uniform' },
    { front: 'Name <strong>3</strong> functions mapping R to R that are <strong>discontinuous at 0</strong>', back: '<strong>Sample Responses:</strong> step function at 0, 1/x, sin(1/x), Dirac delta function at 0' },
  ],

  'Mathematical Physics': [
    { front: 'Name <strong>3</strong> pairs of <strong>observables</strong> to which the <strong>uncertainty principle</strong> applies', back: '<strong>Sample Responses:</strong> position and momentum, time and energy, x- and y-components of angular momentum' },
    { front: 'Name <strong>3</strong> types of <strong>raising/lowering operators</strong> in quantum mechanics', back: '<strong>Sample Responses:</strong> harmonic oscillator, angular momentum, spin, electron number' },
    { front: 'Name <strong>3</strong> formulations of <strong>classical mechanics</strong>', back: '<strong>Sample Responses:</strong> Newtonian, Lagrangian, Hamiltonian' },
    { front: 'Name <strong>3</strong> classes of <strong>special functions</strong> arising in physics', back: '<strong>Sample Responses:</strong> Bessel functions, Legendre polynomials, Laguerre polynomials, Hermite polynomials' },
    { front: 'Name <strong>3 noninertial forces</strong> in a <strong>rotating reference frame</strong>', back: '<strong>Sample Responses:</strong> centrifugal, Coriolis, tangential noninertial' },
    { front: 'Name <strong>3</strong> systems that exhibit the <strong>harmonic oscillator</strong> in some parameter or configuration regime', back: '<strong>Sample Responses:</strong> spring-mass system, simple pendulum, LC circuit' },
    { front: 'Name <strong>3</strong> 2-by-2 <strong>Hermitian</strong> matrices', back: '<strong>Sample Responses:</strong> Pauli X, Y and Z, Hadamard' },
    
  ],

};

function createFsrCard(card) {
  const cardEl = document.createElement('div');
  cardEl.className = 'fsr-card';
  cardEl.innerHTML = `
    <div class="fsr-card-inner">
      <div class="fsr-card-front">
        <p>${card.front}</p>
      </div>
      <div class="fsr-card-back">
        <p>${card.back}</p>
      </div>
    </div>
  `;
  
  cardEl.addEventListener('click', function() {
    this.classList.toggle('fsr-card-flipped');
  });
  
  return cardEl;
}

function displayFsrTheme(themeName) {
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  currentIndex = 0;

  renderSingleCard();

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  });
}

function initializeFsr() {
  const menu = document.getElementById('fsr-menu');
  
  const menuTitle = document.createElement('h3');
  menuTitle.className = 'fsr-menu-title';
  menuTitle.textContent = 'Categories';
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      btn.classList.add('fsr-active');
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}

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  const card = cards[currentIndex];

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  nav.className = 'fsr-nav';

  const prevBtn = document.createElement('button');
  prevBtn.textContent = '❮ Prev';

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  nextBtn.textContent = 'Next ❯';

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  counter.textContent = `${currentIndex + 1} / ${cards.length}`;

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```