Foundations of Algorithmic Thinking: The Mathematics Underneath Every Line of Code (The Computing Series)

See the structure underneath every system you build.A database index becomes a tree. A cache becomes a priority queue. A load balancer becomes a hash function. Foundations of Algorithmic Thinking gives working software engineers the vocabulary to name what their code actually is — so design reviews, system design interviews, and the next architecture you build stop being guesswork.WHAT YOU'LL BE ABLE TO DOName the structure of any algorithm or data structure you encounter — sorting, searching, hashing, graph algorithms, recursion, dynamic programming, probability — and reason about why it works, not just that it works.Apply Big-O notation in practice, not just on a whiteboard. Know why merge sort is O(n log n), why your hash table sometimes degrades to O(n), and what those numbers mean in wall-clock time at production scale.Spot the right tradeoff in design reviews — latency vs throughput, consistency vs availability, simplicity vs flexibility. Ten architectural tradeoffs covered in depth.Recognise the failure pattern before it ships — cascading failure, thundering herd, schema drift, hotspotting. Twelve failure modes that cover almost every production incident.Hold a complete map of computing's foundations — logical reasoning, set theory, complexity analysis, algorithm design, data structures, graphs, and discrete mathematics — in a single readable volume.WHO THIS BOOK IS FORSoftware engineers, backend developers, and computer science learners with a few years of practice who can write the code but want to understand the mathematical structure beneath it. Also a focused resource for senior software engineer interviews, staff engineer reviews, and system design interview preparation — where structural reasoning matters more than puzzle-solving.WHAT'S INSIDE40 chapters across 5 parts — logical reasoning, set theory and functions, complexity analysis and algorithm design, data structures and graphs, and discrete mathematics.120 exercises at three levels — Understand, Apply, Design. Designed for self-study and interview preparation.12 recurring threads — hashing, trees, graphs, queues, caching, redundancy, state machines, divide and conquer, consensus, encoding, feedback loops, tradeoffs. Patterns that appear at every layer of computing.Compression blocks at the end of every chapter — a one-page structured recap so the book stays useful as a reference.TOPICS COVEREDLogic and propositional calculus · truth tables · proof techniques · mathematical induction · set theory · functions and relations · sequences and recurrences · matrices · algorithm analysis · Big-O notation · recurrence relations · divide and conquer · dynamic programming · arrays and hash tables · stacks, queues, and linked structures · trees, BSTs, heaps · balanced trees and B-trees · graph representation · BFS, DFS · shortest paths · topological sort · minimum spanning trees · combinatorics · probability · expected value · randomised algorithms · number theory · modular arithmetic · cryptography and RSA.ABOUT THE SERIESBook 1 of The Computing Series — an eight-book curriculum that builds a complete computer science and software engineering, covering algorithm engineering, infrastructure patterns, system design, code architecture, technology leadership, and product strategy. Book 0 (The Engineer's Map) is the reference companion to the whole series.ABOUT THE AUTHORHarish Kumar is a software engineer and systems thinker. The Computing Series compresses the full stack of engineering knowledge — from first principles to product strategy — into one connected learning system.