Technical Fundamentals & Core Skills Topics
Core technical concepts including algorithms, data structures, statistics, cryptography, and hardware-software integration. Covers foundational knowledge required for technical roles and advanced technical depth.
Mathematical Foundations and Theory
Evaluation of mastery over the mathematical and theoretical tools relevant to the candidate s work, including comfort with formal notation, derivations, proofs or sketches of proofs, and reasoning about properties such as convergence, complexity, and generalization. Candidates should be able to derive critical steps, explain assumptions, and discuss theoretical trade offs between approaches.
Data Structures and Complexity
Comprehensive coverage of fundamental data structures, their operations, implementation trade offs, and algorithmic uses. Candidates should know arrays and strings including dynamic array amortized behavior and memory layout differences, linked lists, stacks, queues, hash tables and collision handling, sets, trees including binary search trees and balanced trees, tries, heaps as priority queues, and graph representations such as adjacency lists and adjacency matrices. Understand typical operations and costs for access, insertion, deletion, lookup, and traversal and be able to analyze asymptotic time and auxiliary space complexity using Big O notation including constant, logarithmic, linear, linearithmic, quadratic, and exponential classes as well as average case, worst case, and amortized behaviors. Be able to read code or pseudocode and derive time and space complexity, identify performance bottlenecks, and propose alternative data structures or algorithmic approaches to improve performance. Know common algorithmic patterns that interact with these structures such as traversal strategies, searching and sorting, two pointer and sliding window techniques, divide and conquer, recursion, dynamic programming, greedy methods, and priority processing, and when to combine structures for efficiency for example using a heap with a hash map for index tracking. Implementation focused skills include writing or partially implementing core operations, discussing language specific considerations such as contiguous versus non contiguous memory and pointer or manual memory management when applicable, and explaining space time trade offs and cache or memory behavior. Interview expectations vary by level from selecting and implementing appropriate structures for routine problems at junior levels to optimizing naive solutions, designing custom structures for constraints, and reasoning about amortized, average case, and concurrency implications at senior levels.
Coding Fundamentals and Problem Solving
Focuses on algorithmic thinking, data structures, and the process of solving coding problems under time constraints. Topics include core data structures such as arrays, linked lists, hash tables, trees, and graphs, common algorithms for searching and sorting, basics of dynamic programming and graph traversal, complexity analysis for time and space, and standard coding patterns. Emphasis on a disciplined problem solving approach: understanding the problem, identifying edge cases, proposing solutions with trade offs, implementing clean and readable code, and testing or reasoning about correctness and performance. Includes debugging strategies, writing maintainable code, and practicing medium difficulty interview style problems.
Linear Algebra and Matrix Operations
Fundamental linear algebra concepts used throughout machine learning and data analysis. Topics include vector and matrix operations, linear transformations, matrix multiplication properties, eigenvalues and eigenvectors, singular value decomposition, principal component analysis, matrix factorizations, diagonalization, and how these concepts underpin algorithms such as linear models, embeddings, and matrix factorization methods.
Complexity Analysis and Tradeoffs
Evaluating algorithmic complexity and engineering trade offs between time, space, maintainability, and operational cost. Candidates should be able to express complexity using big O notation, reason about amortized cost, identify bottlenecks, compare alternative solutions and explain when to optimize or accept higher complexity. Include discussion of measurement, profiling, and pragmatic trade offs such as caching versus recomputation or memory versus latency.
Intermediate Algorithm Problem Solving
Practical skills for solving medium difficulty algorithmic problems. Topics include two pointer techniques, sliding window, variations of binary search, medium level dynamic programming concepts such as recursion with memoization, breadth first search and depth first search on graphs and trees, basic graph representations, heaps and priority queues, and common string algorithms. Emphasis is on recognizing problem patterns, constructing correct brute force solutions and then applying optimizations, analyzing trade offs between time and space, and practicing systematic approaches to reach optimal or near optimal solutions.
Problem Solving and Structured Thinking
Focuses on general problem solving strategies and structured thinking applicable to engineering, coding, and complex decision making. Core skills include clarifying the problem, breaking problems into subproblems, identifying patterns, selecting appropriate approaches and data structures, developing and testing incremental solutions, analyzing trade offs, reasoning about time and space complexity, handling edge cases, and communicating thought process clearly. Includes algorithmic patterns and design of systematic approaches to unfamiliar problems as well as frameworks for organizing thought under ambiguity.
Mathematical Reasoning and Derivations
Comfort and proficiency with formal mathematical reasoning used in research. Candidates should be able to perform derivations by hand, manipulate equations, apply calculus and linear algebra, reason about optimization and convergence properties, use probability and expectation operations, derive bounds and error estimates, and write concise proofs using common techniques such as induction and contradiction. Interviewers may probe correctness, clarity of steps, and understanding of the assumptions that underlie derivations.
Theoretical Foundations of Machine Learning
Covers the mathematical and theoretical building blocks that underpin modern machine learning and artificial intelligence. Key areas include probability theory and Bayesian reasoning such as conditional probability, Bayes theorem, expectation and variance, and probabilistic inference; linear algebra and matrix analysis including eigenvalues, eigenvectors, matrix decompositions, matrix norms, rank, and geometric intuitions; optimization and calculus topics such as gradient descent, stochastic optimization, convexity, Lagrange multipliers, partial derivatives, the chain rule, and properties of optimization landscapes; and related theoretical themes such as information theory and approximation concepts. Candidates should be able to connect these foundations to algorithm behavior, model expressivity, convergence properties, and practical design decisions.