Mathematics for Programming
How much math should i know? The answer is school level mathematics is enough to start and solve easy to medium level problem solving.
Arithmetic Basics
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Addition (+), Subtraction (-), Multiplication (*), Division (/): Loops, counters, scaling data; beware integer vs. float division (e.g., 5/2=2 vs 2.5).
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Modulus (%): Remainders for even/odd (
n % 2), cycles, hashing; your “even-mod” is too narrow. -
Exponents/Powers (^ or **): Growth models, array sizing (e.g., 2^n for bit shifts); absent in your list, causes exponential bugs.
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Absolute value (
|x|): Distances, error metrics; trivial but frequently botched.
Number Theory
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Divisibility checks (n % k == 0): Factors, grouping; extend to GCD via Euclidean algorithm.
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Prime/composite numbers: Identify via trial division up to √n.
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Divisor counting: Sum divisors efficiently (O(√n)); blind loops timeout on large inputs.
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Primality tests: Basic trial division or Sieve of Eratosthenes for ranges; O(n log log n) beats your implied brute force.
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Binary/Number systems (
base 2, octal, hex): Bitwise ops (& | ^ ~ >> <<), masks, flags.
Logic and Booleans
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Boolean logic (
AND &&, OR ||, NOT !, XOR): Conditions, filters, state machines; no program runs without this. -
Truth tables: Evaluate expressions.
Probability and Counting
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Basic probability (events, odds): Simulations, randomness (e.g.,
random()seeds); define P(A) = favorable/total. -
Combinations (C(n,k)), Permutations (P(n,k)): Sampling, shuffling; off-by-1 errors kill naive factorials.
Geometry and Coordinates
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Coordinate systems (Cartesian x,y): Graphics, maps (e.g., distance = √((x2-x1)² + (y2-y1)²)).
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Basic geometry: Angles (radians for trig funcs), area/perimeter; vectors for direction (dx, dy).
Algorithms Foundations
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Order of operations (PEMDAS/BODMAS): Expression evaluation; precedence bugs crash code.
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Min/max, rounding (floor/ceil): Data bounds, normalization.
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Sums/products (sigma notation basics): Accumulators, stats.