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Foundations of Computer Science

Course Orientation and Core Principles

Mathematical Preliminaries for CS

Algorithms and Data Structures

Algorithm Design Paradigms

Core Data Structures and Abstract Data Types

Algorithm Analysis and Complexity

Software Construction and Abstraction

Abstraction, Modularity, and Interfaces

Correctness, Testing, and Verification

Systems and Computation Models

Computer Systems Essentials

Models of Computation and Languages

Capstone Integration and Assessment

Integrated Design Challenge

Quiz: Mathematical Foundations and Asymptotics

Quiz: Algorithm Design Paradigms and Correctness

Quiz: Data Structures and Trade-offs

Quiz: Graph and Optimization Algorithms

Quiz: Systems, Models of Computation, and Complexity

End-of-Course Survey

Applied Computer Science: Algorithms, Data Structures, and Scalable Design is a practical, theory-grounded course that teaches you how to specify, design, analyze, and implement solutions that scale. You’ll build a strong foundation in logic, proofs, asymptotics, and recurrences, then apply these tools to real problems using core algorithmic paradigms—divide and conquer, greedy methods, dynamic programming, and backtracking. Along the way, you’ll master essential data structures (arrays, lists, stacks, queues, heaps, hash tables, trees, graphs) and learn to reason about trade-offs between time, space, and implementation complexity. Beyond algorithms, the course brings software construction to the forefront: abstraction, contracts, interfaces, testing, and verification. You’ll also gain systems intuition—how programs run, how memory and concurrency affect performance, and how computational models set the limits of what’s possible. The capstone challenges you to integrate everything: define requirements, set performance targets, choose and justify designs, and validate them through testing and empirical analysis. If you want to move from solving small coding tasks to engineering robust, scalable solutions, this course gives you the mental models, vocabulary, and techniques to do it with confidence.

Applied Computer Science: Algorithms, Data Structures, and Scalable Design

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            <p>Applied Computer Science: Algorithms, Data Structures, and Scalable Design builds a rigorous pathway from foundational principles to practical, scalable software design. The course begins by clarifying what computation means and how abstraction, specification, and correctness anchor professional problem solving. You will learn to frame problems through a disciplined workflow—specification → design → analysis → implementation → verification—then revisit that workflow across running examples that connect theory to practice. Along the way, mathematical preliminaries such as logic, proofs, sets and functions, counting, asymptotic notation, and recurrences provide the language and tools to reason precisely about behavior and performance.</p>

<p>With this foundation, the course explores algorithmic thinking and core data structures as unifying themes. You will study design paradigms including divide and conquer, greedy methods, dynamic programming, and backtracking, backed by correctness techniques like loop invariants and induction. Arrays, lists, stacks, queues, heaps, balanced trees, hash tables, tries, and graphs are treated as abstract data types with clear interfaces and analyzed for time–space trade-offs, including amortized costs. Complexity analysis—including tight bounds, best/average/worst-case perspectives, and space models—prepares you to evaluate designs, while graph problems (shortest paths, spanning trees) and the limits of computation (P vs. NP, reductions, approximation) sharpen your judgment about tractability.</p>

<p>Software construction is treated as a first-class concern: you will practice information hiding, contracts, and API design to achieve modularity and reuse. The course emphasizes correctness through systematic testing, assertions, invariants, and an introduction to formal verification, complemented by pragmatic debugging, regression testing, and a continuous integration mindset. Systems content connects algorithm choices to real execution: compilation and interpretation, memory hierarchies and locality, and conceptual concurrency inform how implementations scale and where bottlenecks arise.</p>

<p>Broader models of computation and language paradigms round out your mental toolkit. High-level coverage of automata, grammars, and Turing machines illuminates what can and cannot be computed, while contrasts among imperative, functional, and object-oriented styles—along with type systems and static versus dynamic checks—show how language design shapes reasoning and safety. The capstone Integrated Design Challenge asks you to specify a real-world problem, select and justify algorithms and data structures using asymptotic and empirical evidence, and plan a thorough testing and verification strategy. A series of targeted quizzes reinforce mathematical foundations, design paradigms, data structure trade-offs, graph and optimization concepts, and systems and complexity, preparing you to design correct, efficient, and scalable software.</p>
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