Core Skills Guide for AI Interviews (Math, Code, SQL) 2025

🛠️

Success in AI and ML interviews demands mastery of three pillars: mathematical intuition, programmatic problem-solving, and data query fluency.
This guide aligns these core competencies into one cohesive learning path — from the calculus behind backpropagation to the SQL powering data insights.

💡 Why focus on these pillars?

Top-tier interviews test across three foundations:

Math Foundations → To prove you understand the why behind algorithms.
Coding & Algorithms → To demonstrate practical logic and efficiency.
SQL & Analytics → To extract and reason over real-world data.

Master these, and you’ll speak the universal language of AI problem-solving.

📐 Mathematics for Machine Learning

What’s covered here?

This section builds your mathematical intuition — from the geometry of vectors to the gradients that drive neural optimization.
These are the skills that let you derive algorithms, debug training instability, and discuss model design rigorously.

Linear Algebra — The Geometry of Data

Vectors & Operations

The atomic unit of data representation — direction, magnitude, and inner products.

Matrix Operations

Matrix multiplication, transformations, and dot-product geometry.

Eigenvalues, Eigenvectors & SVD

The backbone of PCA, transformations, and data compression.

PCA & Dimensionality Reduction

Extract key features and reduce data dimensionality efficiently.

→ View Full Math Roadmap

Complete roadmap for Linear Algebra, Calculus, and Optimization.

Calculus & Optimization — The Engine of Learning

Derivatives & Gradients

Understand rate of change and gradient flow in model parameters.

Chain Rule & Backpropagation

Trace gradient flow through computation graphs.

Optimization & Convexity

Gradient descent, convex surfaces, and global minima intuition.

Gradient-Based Optimization

Adaptive optimizers, tuning, and convergence diagnostics.

→ View Full Math Roadmap

Comprehensive roadmap for calculus and optimization.

🎲 Probability & Statistics

What’s covered here?

Probability and statistics give AI engineers their quantitative intuition for uncertainty — the foundation for reasoning, inference, and model evaluation.
This section helps you translate theory into confidence intervals, hypothesis tests, and data-backed reasoning.

Probability — Modeling Uncertainty

Conditional Probability

Quantifying dependence and updating beliefs with new evidence.

Bayes’ Theorem

Connecting priors, likelihoods, and posteriors — core of Bayesian inference.

Continuous Distributions

Understand Gaussian, Exponential, and Uniform distributions.

Maximum Likelihood Estimation

Deriving parameters that best fit observed data.

→ View Full Probability & Statistics Roadmap

Master probability theory and inference systematically.

Statistics — Drawing Reliable Conclusions

Sampling & Estimation

Building estimators and understanding sampling variability.

Hypothesis Testing

Nulls, alternatives, and interpreting statistical significance.

Covariance & Correlation

Measure relationships — and understand when they mislead.

Resampling & Validation

Bootstrap, cross-validation, and reliability estimation.

→ View Full Statistics Roadmap

Comprehensive guide to inference and statistical reasoning.

🗃️ SQL + Analytics

Why SQL mastery matters

Machine learning begins with data understanding. SQL fluency demonstrates you can extract, join, and summarize massive datasets efficiently — an essential step before model building.

🧩 Block 1 — Core Concepts & Optimization

Core SQL Concepts

1️⃣ SQL Query Lifecycle

Understand the logical flow: FROM → WHERE → GROUP → SELECT.

2️⃣ Filtering & Aggregation

Master WHERE vs HAVING and aggregation logic.

3️⃣ Nulls & Conditional Logic

Handle NULLs, CASE statements, and Boolean logic correctly.

4️⃣ SQL Joins

Understand INNER, LEFT, RIGHT, and FULL joins through intuition.

Performance & Optimization

5️⃣ Execution Plans

Interpret EXPLAIN ANALYZE and query cost breakdowns.

6️⃣ Indexing for Speed

Leverage indexes wisely to improve query performance.

7️⃣ CTEs & Refactoring

Simplify logic using reusable subqueries with WITH clauses.

8️⃣ Common SQL Pitfalls

Avoid costly anti-patterns like SELECT * and unindexed filters.

📊 Block 2 — Analytics & Design

Analytical SQL

9️⃣ Window Functions & Analytics

RANK, DENSE_RANK, SUM OVER — mastering analytical queries.

🔟 Cohort & Retention Analysis

Measure retention, churn, and funnel metrics using SQL.

1️⃣1️⃣ Time-Series & Lag Analysis

Use LAG, LEAD, and moving averages to analyze trends.

Database Design

1️⃣2️⃣ Normalization & Normal Forms

1NF–3NF — remove redundancy and preserve integrity.

1️⃣3️⃣ Star & Snowflake Schemas

Design analytics-ready data warehouses for scalability.

1️⃣4️⃣ Data Integrity & Keys

Understand primary, foreign, and surrogate keys in relational design.

📘 Pro Tip:
Pair each SQL concept with a hands-on exercise on an open dataset (e.g., Kaggle’s data) to internalize query logic and optimization thinking.

💻 Coding Interview Prep

What’s covered here?

These are the most essential coding problems every top-tech candidate should master.
Each category tests a distinct reasoning pattern — arrays, recursion, DP, or graphs — that frequently appear in top-companies interviews.
These problems are drawn from the Blind 75 list — the gold standard for interview readiness.

🧠 Block 1 — Arrays, Strings & Linked Lists

Arrays / Two Pointers / Hashing

1️⃣ 3Sum

Find all unique triplets that sum to zero.

2️⃣ Container With Most Water

Maximize area between two vertical lines.

3️⃣ Longest Consecutive Sequence

Find longest sequence of consecutive integers.

Strings

4️⃣ Longest Substring Without Repeating Characters

Longest substring of unique characters.

5️⃣ Minimum Window Substring

Find smallest substring containing all required chars.

Linked Lists

6️⃣ Reverse Linked List

Reverse a singly linked list.

7️⃣ Linked List Cycle

Detect a cycle in linked list using two pointers.

8️⃣ Merge Two Sorted Lists

Merge two sorted linked lists into one.

🔢 Block 2 — DP, Trees & Backtracking

Dynamic Programming (DP)

9️⃣ Climbing Stairs

Count ways to reach top of staircase.

🔟 House Robber

Maximize loot without robbing adjacent houses.

1️⃣1️⃣ Longest Palindromic Substring

Find longest palindrome within a string.

1️⃣2️⃣ Coin Change

Minimum coins to make target amount.

1️⃣3️⃣ Partition Equal Subset Sum

Determine if array can be partitioned into equal sums.

Trees / Binary Trees / BST

1️⃣4️⃣ Binary Tree Level Order Traversal

Traverse tree level by level using BFS.

1️⃣5️⃣ Diameter of Binary Tree

Find longest path between any two nodes.

1️⃣6️⃣ Lowest Common Ancestor of a BST

Find lowest common ancestor node in BST.

Backtracking

1️⃣7️⃣ Subsets

Generate all possible subsets of a set.

1️⃣8️⃣ Combination Sum

Find all combinations that sum to target.

1️⃣9️⃣ Word Search

Check if word exists in character grid.

🧩 Block 3 — Stack & Graphs

Stack

2️⃣0️⃣ Valid Parentheses

Check if brackets are properly nested.

2️⃣1️⃣ Daily Temperatures

Find how many days until a warmer temperature.

Graphs / BFS / DFS / Union-Find

2️⃣2️⃣ Number of Islands

Count connected components in grid using DFS.

2️⃣3️⃣ Clone Graph

Deep copy an undirected graph using DFS/BFS.

2️⃣4️⃣ Course Schedule

Detect cycle in directed graph using topological sort.

2️⃣5️⃣ Redundant Connection

Find edge causing a cycle in graph.

Disclaimer:
Problem titles listed here are sourced from LeetCode, and each link directs to their official problem page.
All problem descriptions, examples, and editorials are © LeetCode and their respective authors.