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A Guide to the Indian National AI Olympiad

SOTA – AI Community · a companion to the IOAI Guide

Abstract

INAIO selects and trains the students who represent India at IOAI. This guide follows its stages in order. Stage 1 starts with an introduction and a word of advice, then covers mathematical and logical reasoning across twelve topics, from numerical foundations to graph algorithms. Guides for the later stages will follow. For what INAIO is and how its stages fit together, read Introduction to INAIO in the IOAI Guide. Mark modules as you read them, and your progress is saved in this browser.

5 stages 70 modules 0 of 70 done

Stage 1 · Mathematical and logical reasoning

0 of 70 done

0Start here

  1. 0.1 Introduction to Stage 1
  2. 0.2 Word of Advice

1Numerical Foundations

  1. 1.1 Fractions, ratios and percentages
  2. 1.2 Powers, roots and logarithms
  3. 1.3 Absolute values and inequalities
  4. 1.4 Averages and summations
  5. 1.5 Floor, ceiling and rounding
  6. Test Numerical Foundations test 40 questions · 100 min

2Algebra and Equations

  1. 2.1 Simplifying expressions
  2. 2.2 Linear equations and systems
  3. 2.3 Solving quadratic equations
  4. 2.4 Linear and quadratic inequalities
  5. 2.5 Word problems into equations
  6. 2.6 Constraints and feasibility
  7. Test Algebra and Equations test 48 questions · 120 min

3Functions and Graphs

  1. 3.1 Function notation and transforms
  2. 3.2 Linear and quadratic functions
  3. 3.3 Exponential and log functions
  4. 3.4 Trigonometry and periodicity
  5. 3.5 Piecewise and indicator functions
  6. 3.6 Functions from their graphs
  7. Test Functions and Graphs test 48 questions · 120 min

4Sequences and Recurrences

  1. 4.1 Arithmetic and geometric sequences
  2. 4.2 Differences and patterns
  3. 4.3 Recurrence relations
  4. 4.4 Iterative state updates
  5. 4.5 Growth, decay and transitions
  6. Test Sequences and Recurrences test 40 questions · 100 min

5Calculus and Optimisation

  1. 5.1 Basic differentiation
  2. 5.2 Maxima and minima
  3. 5.3 Convex and quadratic optimisation
  4. 5.4 Constrained optimisation
  5. 5.5 Absolute and squared distances
  6. Test Calculus and Optimisation test 40 questions · 100 min

6Logic and Deductive Reasoning

  1. 6.1 Propositional logic
  2. 6.2 Implications and contrapositives
  3. 6.3 Necessary and sufficient
  4. 6.4 Consistency and counterexamples
  5. 6.5 Case analysis and elimination
  6. 6.6 Constraint-based puzzles
  7. Test Logic and Deductive Reasoning test Coming soon

7Combinatorics and Discrete Reasoning

  1. 7.1 Counting principles
  2. 7.2 Permutations and combinations
  3. 7.3 Counting with restrictions
  4. 7.4 Parity and invariants
  5. 7.5 Enumeration and casework
  6. 7.6 Worst-case reasoning
  7. Test Combinatorics and Discrete Reasoning test 48 questions · 120 min

8Probability

  1. 8.1 Sample spaces and events
  2. 8.2 Independent and dependent events
  3. 8.3 Conditional probability
  4. 8.4 Total probability and Bayes
  5. 8.5 Complements, inclusion-exclusion
  6. 8.6 Probability trees
  7. Test Probability test 48 questions · 120 min

9Random Variables and Expected Value

  1. 9.1 Discrete random variables
  2. 9.2 Expected value
  3. 9.3 Linearity of expectation
  4. 9.4 Binomial probabilities
  5. 9.5 Waiting-time problems
  6. 9.6 Expected costs and decisions
  7. Test Random Variables and Expected Value test 48 questions · 120 min

10Coordinate Geometry and Vectors

  1. 10.1 Cartesian coordinates
  2. 10.2 Euclidean and Manhattan distance
  3. 10.3 Vectors and vector operations
  4. 10.4 Dot product and cosine similarity
  5. 10.5 Geometry of minimising distance
  6. Test Coordinate Geometry and Vectors test 40 questions · 100 min

11Matrices and Linear Transformations

  1. 11.1 Matrix dimensions and indexing
  2. 11.2 Matrix operations
  3. 11.3 Matrix–vector multiplication
  4. 11.4 Systems and transformations
  5. 11.5 Transition matrices
  6. 11.6 Row and column normalisation
  7. Test Matrices and Linear Transformations test 48 questions · 120 min

12Graph Theory and Algorithms

  1. 12.1 Graph representations
  2. 12.2 Paths, cycles and connectivity
  3. 12.3 Graph traversal and search
  4. 12.4 Grid paths and constraints
  5. 12.5 Strongly connected components
  6. 12.6 Random walks and PageRank
  7. Test Graph Theory and Algorithms test 48 questions · 120 min

Stage 2 · Theory and practical implementation

Coming soon.

Stage 3 · Online coaching and evaluation

Coming soon.

Stage 4 · The national training camp

Coming soon.

Stage 5 · Team preparation

Coming soon.