A Guide to Essential Computer Science Courses

Introduction to Programming

Typically one of the first courses a computer science major takes, this article teaches the basics of coding, problem-solving, and computational thinking. The most commonly used programming languages for this course are Java, C++, and Python. It covers basic syntax, structures, variables, data types, basic input/output, conditionals, loops, functions, basic algorithms, and debugging. Many of the first programs that students create are "Hello World," to-do lists, or calculators. But one of the main skills you get in this course is translating logic into code. Also, being able to solve problems and breaking them down into smaller steps, algorithms, and data structures is a key takeaway.

A cornerstone in computer science is having your programs work as efficiently as possible. Key topics covered in this course are: - Time Complexity: How long it takes for a program to run, measured in Big O, Big Omega, or Big Theta. - Data Structures: Such as arrays, linked lists, stacks, queues, trees, or graphs. - Fundamental Algorithms: Including sorting algorithms like Quicksort, Merge Sort, and Bubble Sort; searching algorithms such as Binary Search and Dijkstra's algorithm; and recursion concepts like the Tower of Hanoi, the Fibonacci sequence, and the Y Combinator.

This course mainly teaches you how to write efficient and scalable code, which is key to many coding interviews. It allows you to tackle LeetCode-style problems and really think about trade-offs when creating programs.

Discrete Mathematics

This is a course that really goes into the foundation of computer science. Just like the name, it's a type of math that focuses on countable, whole, and discrete items. So, you never work with any decimals or complex numbers. It's not like calculus, which is a type of continuous math, as calculus deals with rates of change, growth, or decay.

Some key topics covered are: - Formal Logic: Basically the same type of prop logic you usually see in philosophy courses. - Predicate Logic: A type of logic that deals with absolute or non-absolute statements. - Basic Mathematical Proofs: Such as direct proof, proof by contradiction, proof by cases, or mathematical induction. - It also goes over rigid mathematical definitions of certain terms, such as what it means for a number to be even or odd. - Functions: Such as surjective, injective, and bijective functions. - Elementary Graph Theory, Elementary Set Theory, and Set Operations: Such as union, intersection, and complement. - Elementary Number Theory: Such as modular arithmetic or encryption and basic combinatorics.

Discrete math is a course that really goes over the pure logic of computers. It allows students to really learn the language of computers and really fleshes out how to build programs and think more logically and computationally.

Computer Architecture

A course that bridges the gap between hardware and software. In this course, you learn how a CPU processes instructions, memory input/output, and how high-level code translates into machine language. It also goes into Boolean algebra and logic gates, and combinational versus sequential circuits. You'll also learn how to write with the assembly language.

You'll also touch into: - CPU Design: Such as arithmetic logic units. - Memory Hierarchy: Like SRAM versus DRAM. - GPU Architecture. - Input/Output Systems: Such as storage devices, or hard drives versus solid-state drives.

You'll also use the C programming language in this course. You even might touch into the basics of quantum computing. The main skills that you get are that you learn operating system or kernel development, are able to visualize data flows from CPUs, and work with embedded systems.

Calculus

A math course mainly about rates of change and finding the area and volume of very irregular shapes. Calculus can be divided into two sections: differential calculus and integral calculus.

• Differential Calculus: Deals with concepts such as limits and derivatives. Basically, what does a value do as it gets closer and closer to another value? You'll learn different techniques for finding derivatives, such as the power rule, the product rule, the quotient rule, or the chain rule.
• Integral Calculus: Deals with finding the volume or area under a curve. You'll learn integration techniques such as substitution, integration by parts, and many more.

You'll also learn techniques to find out if a series—which is a sequence of repeated addition or multiplication—converges or diverges. Converging means it gets closer and closer to a certain value or number, while diverging means the answer is infinity. You'll also learn the basics of differential equations, which is a type of problem where the answer is a function. Calculus is extremely useful for machine learning, graphics, and physics engines, and for tracking the growth and speed of algorithms.

Linear Algebra

A mathematics course given to computer science, physics, and engineering majors. Linear algebra is about vectors, matrices, and linear transformations.

• Vectors: Objects in mathematics that, instead of representing a singular point, represent a direction and magnitude. Direction means which way, and magnitude means how long.
• A Matrix: A grid of numbers or values that allows you to solve big and complicated problems by doing math to multiple numbers at once.
• Linear Transformations: Are about transposing 2D planes. It's like if you had a drawing of a smiley face. If you were to stretch, squish, and turn it, but you preserve any straight lines and you transform around a central middle point.

Linear algebra is used for computer graphics and 3D space, machine learning, and even Google's PageRank algorithm.

Databases

A course that teaches students how to interact with, manage, and structure data. This course goes over relational databases with tables, rows, and keys. You learn the SQL or Structured Query Language and learn how to select, insert, update, and delete entries in a database. You also go over database design, such as binary trees and hash tables. You'll even learn to use databases that require no SQL, like Redis or MongoDB. In this course, you'll learn to use tools like MySQL, SQLite, Firebase, and AWS. Learning about databases is crucial for creating records for businesses, managing the backends of websites, and data science.

Networking

This course explores how devices communicate over the internet and the structure of networks. You learn about different protocols like HTTP, TCP/IP, and DNS, and analyze packets with tools like Wireshark. You'll also learn about different network types like WAN, LAN, and VPNs, and network topologies such as star, mesh, and bus. You'll also learn about the OSI model and work with cloud platforms such as AWS and Azure. A computer networking course gives students the tools for cybersecurity, cloud engineering, backend development, and DevOps.

Theory of Computation

A course that touches on more of the theoretical or philosophical aspects of computer science. It explores the limits of what's even possible to compute. It covers topics like: - Finite State Automata: Which is about diagramming the possible actions of machines given certain inputs. - Regular Languages for Finite State Automata: Which is about all the possible inputs. - The concept of a Turing Machine: A theoretical computer that can loop, do conditionals, and hold state.

They'll dive very deep into the topic of algorithmic complexity and explore open questions in computer science such as P versus NP, which is a problem that tries to figure out if computational problems that are easy to verify are also easy to solve. You'll probably also touch on the halting problem, which is a thought experiment that answers the question if it's possible for a program to check if another program runs infinitely or not. Theory of computation teaches students the limits of computing, security, and hardware design.

Probability and Statistics

This course focuses on quantifying and analyzing data and also how to make data-driven decisions. You learn the fundamentals of probability and basic set theory. You also learn about Bayes' theorem, which is a type of conditional probability in which it calculates the probability of something happening given the fact that something else has already happened. You'll likely delve into probability distributions such as the normal distribution or the Poisson distribution. You'll work with data visualization tools such as histograms, box plots, or scatter plots. Students often work with statistical concepts such as the central limit theorem, confidence intervals, p-values, or effect sizes. Students often use software such as pandas, SciPy, and Matplotlib, which are Python libraries. You'll likely learn how to code in the R programming language. You'll also use Microsoft Excel a lot. A course in probability and statistics is crucial for computer science majors because it's essential if you want to go into machine learning, use algorithms, or data science.

Machine Learning

A course that teaches students how to work with or create AI. It teaches students how computers can learn from information given to them. It focuses on neural networks and how they work, touching on topics such as backpropagation, activation functions, natural language processing, and deep learning. Machine learning tends to be Python-dominant, but you can also use other languages as well. You make use of many Python libraries such as scikit-learn, TensorFlow, and PyTorch. A course in machine learning is quite advanced, so your prerequisites are usually other programming courses, linear algebra, and calculus. A course in machine learning prepares computer science majors for AI careers or even other fields like healthcare for diagnosis and finance for fraud detection.

Cybersecurity

A course that gives students the tools to protect computer systems from digital attacks. It goes over vulnerability defenses and white-hat hacking. Students will understand different types of cyberattacks such as DoS, phishing, or cross-site scripting, and different types of defenses such as firewalls and encryption. You'll go over legal and ethical issues of privacy and disclosure and threat modeling like the STRIDE model, which is a system designed to identify the type of security threat to a system. Students learn to use tools such as Metasploit and Nmap for penetration testing. Penetration testing is what it sounds like: hiring someone to intentionally hack a system to see how vulnerable it is. Cybersecurity not only relies on a knowledge of security flaws involving computers but also the type of security risks that don't involve computers, such as social engineering. A course in cybersecurity is important for computer science majors because it is a field in high demand, with jobs in healthcare, government, and finance.

Computer Graphics and Game Development

Often an elective, it teaches students how to build and develop 2D and 3D games. Students learn to build using game engines such as Godot, Unity, and Unreal. You also learn how to use graphics APIs such as OpenGL or the Open Graphics Library. You go over key concepts in gaming such as game loops, physics (such as collision detection), and AI (such as pathfinding and behavior trees). You'll also use 3D modeling tools such as Blender and Maya, and do animation such as skeletal rigging, key framing, and even motion capture. This course is not only good for getting into the gaming industry but also for getting into filmmaking, virtual or augmented reality, and even in the medical field for creating simulations.

Embedded Systems and the Internet of Things

A course that marries hardware and software to design and program embedded systems such as microcontrollers and sensors. You'll learn to understand IoT architectures such as edge computing and cloud integration. You'll go into different wireless protocols such as Wi-Fi and Bluetooth and use tools like the Arduino or PlatformIO. This is a field in growing demand with its applications in smart homes, wearables, IoT development, and robotics.

Big Data and Data Science

An interdisciplinary blend of statistics, programming, and machine learning. And you use all of these to learn how to get insights from data. The goal is for students to learn the data science pipeline, which is collection, cleaning, analysis, visualization, and storytelling. You mostly use the Python, R, and SQL languages and use big data tools such as Spark and Hadoop. This course gives students the skills to seek high-demand jobs in tech, finance, and healthcare.