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Mathematics for Computing

Essential mathematics and logic for programmers

89 structured topics, each reinforced with plain-language teaching, memory hooks, hands-on practice, retrieval, teach-back, speed recall, professional transfer and spaced review.

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How mastery works

1. Five-year-old simple

Every new term is explained without assumed knowledge and linked to a familiar picture.

2. Do it

Guided labs, typing, diagrams, configurations, queries or professional artefacts turn words into usable skill.

3. Retrieve it

No-peeking recall, teach-back and 60-second checks force the brain to retrieve instead of recognise.

4. Use it professionally

Failure modes, security, evidence, capstones and spaced repetition build degree and workplace fluency.

Course topics

  1. Number Systems Overview — Decimal, binary, octal, hex
  2. Decimal System — Base-10 fundamentals
  3. Binary System — Base-2 representation
  4. Counting in Binary — Binary sequences
  5. Binary Addition — Adding binary numbers
  6. Binary Subtraction — Subtracting binary numbers
  7. Binary Multiplication — Multiplying binary numbers
  8. Binary Division — Dividing binary numbers
  9. Two's Complement — Signed number representation
  10. One's Complement — Alternative signed format
  11. Octal System — Base-8 representation
  12. Hexadecimal System — Base-16 representation
  13. Hex Conversions — Hexadecimal conversions
  14. Binary to Hex — Direct conversion method
  15. Hex to Binary — Reverse conversion
  16. Octal Conversions — Converting octal numbers
  17. Floating Point Intro — Real number representation
  18. IEEE 754 Standard — Single and double precision
  19. Mantissa & Exponent — Components of floating point
  20. Precision Issues — Rounding errors and limits
  21. Logic Gates Intro — Digital logic fundamentals
  22. AND Gate — Conjunction operation
  23. OR Gate — Disjunction operation
  24. NOT Gate — Negation operation
  25. XOR Gate — Exclusive OR
  26. NAND & NOR Gates — Universal gates
  27. Combined Gates — Building complex circuits
  28. Truth Tables — Boolean expressions
  29. Boolean Algebra Basics — Laws and identities
  30. De Morgan's Laws — NOT of AND/OR
  31. Simplification — Reducing expressions
  32. Karnaugh Maps — Visual simplification
  33. Sum of Products — SOP form
  34. Product of Sums — POS form
  35. Sets Introduction — Set notation and membership
  36. Set Operations — Union, intersection, complement
  37. Set Difference — A - B operation
  38. Symmetric Difference — XOR for sets
  39. Venn Diagrams — Visualizing sets
  40. Subsets & Power Sets — Set relationships
  41. Cartesian Product — Set pairs
  42. Probability Basics — Events and outcomes
  43. Sample Space — All possible outcomes
  44. Probability Rules — Addition and multiplication
  45. Conditional Probability — P(A|B) and Bayes
  46. Bayes' Theorem — Updating probabilities
  47. Independence — Independent events
  48. Expected Value — Mean of random variable
  49. Graph Theory Intro — Vertices, edges, notation
  50. Types of Graphs — Directed, undirected, weighted
  51. Graph Representation — Adjacency matrix/list
  52. Paths & Cycles — Walks, trails, paths
  53. Connectivity — Connected components
  54. Graph Properties — Degree, density, planarity
  55. Tree Structures — Rooted trees, hierarchy
  56. Binary Trees — At most two children
  57. Binary Search Trees — Ordered tree structure
  58. Tree Traversal — Inorder, preorder, postorder
  59. Balanced Trees — AVL and height balance
  60. Spanning Trees — MST algorithms
  61. Graph Algorithms Intro — Common graph problems
  62. Breadth-First Search — Level-order exploration
  63. Depth-First Search — Stack-based exploration
  64. Dijkstra's Algorithm — Shortest paths
  65. Topological Sort — Ordering DAG nodes
  66. Big-O Notation — Time complexity basics
  67. O(1) and O(n) — Constant and linear time
  68. O(log n) — Logarithmic complexity
  69. O(n²) and O(n³) — Polynomial complexity
  70. O(2^n) — Exponential complexity
  71. Complexity Comparison — Comparing growth rates
  72. Space Complexity — Memory usage analysis
  73. Functions — Domain, range, composition
  74. Types of Functions — Injective, surjective, bijective
  75. Relations — Binary relations and properties
  76. Equivalence Relations — Reflexive, symmetric, transitive
  77. Algebra Fundamentals — Variables, equations, PEMDAS
  78. Linear Equations — Solving equations
  79. Matrices Introduction — Matrix notation
  80. Matrix Operations — Add, subtract, multiply
  81. Identity Matrix — Special matrices
  82. Matrix Inverse — Inverse calculation
  83. Statistics Introduction — Descriptive and inferential
  84. Mean, Median, Mode — Measures of central tendency
  85. Range & Variance — Measures of spread
  86. Standard Deviation — Variability measure
  87. Normal Distribution — Bell curve
  88. Correlation — Linear relationships
  89. Hypothesis Testing — Statistical significance

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