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Discrete Mathematics: An Open Introduction updated to 4th edition |
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README.md |
Contents
Summary
The OSSU curriculum is a complete education in computer science using online materials. It's not merely for career training or professional development. It's for those who want a proper, well-rounded grounding in concepts fundamental to all computing disciplines, and for those who have the discipline, will, and (most importantly!) good habits to obtain this education largely on their own, but with support from a worldwide community of fellow learners.
It is designed according to the degree requirements of undergraduate computer science majors, minus general education (non-CS) requirements, as it is assumed most of the people following this curriculum are already educated outside the field of CS. The courses themselves are among the very best in the world, often coming from Harvard, Princeton, MIT, etc., but specifically chosen to meet the following criteria.
Courses must:
- Be open for enrollment
- Run regularly (ideally in self-paced format, otherwise running multiple times per year)
- Be of generally high quality in teaching materials and pedagogical principles
- Match the curricular standards of the CS 2013: Curriculum Guidelines for Undergraduate Degree Programs in Computer Science
When no course meets the above criteria, the coursework is supplemented with a book. When there are courses or books that don't fit into the curriculum but are otherwise of high quality, they belong in extras/courses or extras/readings.
Organization. The curriculum is designed as follows:
- Intro CS: for students to try out CS and see if it's right for them
- Core CS: corresponds roughly to the first three years of a computer science curriculum, taking classes that all majors would be required to take
- Advanced CS: corresponds roughly to the final year of a computer science curriculum, taking electives according to the student's interests
- Final Project: a project for students to validate, consolidate, and display their knowledge, to be evaluated by their peers worldwide
Duration. It is possible to finish within about 2 years if you plan carefully and devote roughly 20 hours/week to your studies. Learners can use this spreadsheet
to estimate their end date. Make a copy and input your start date and expected hours per week in the Timeline
sheet. As you work through courses you can enter your actual course completion dates in the Curriculum Data
sheet and get updated completion estimates.
Warning: While the spreadsheet is a useful tool to estimate the time you need to complete this curriculum, it may not be up-to-date with the curriculum. Use the spreadsheet just to estimate the time you need. Use the OSSU CS website or the repo to see what courses to do.
Cost. All or nearly all course material is available for free. However, some courses may charge money for assignments/tests/projects to be graded. Note that both Coursera and edX offer financial aid.
Decide how much or how little to spend based on your own time and budget; just remember that you can't purchase success!
Process. Students can work through the curriculum alone or in groups, in order or out of order.
- We recommend doing all courses in Core CS, only skipping a course when you are certain that you've already learned the material previously.
- For simplicity, we recommend working through courses (especially Core CS) in order from top to bottom. Some students choose to study multiple courses at a time in order to vary the material they are working on is a day/week. A popular option is to take the math courses in parallel with the introductory courses. Course prerequisites are listed to help you determine if you are prepared for a given course.
- Courses in Advanced CS are electives. Choose one subject (e.g. Advanced programming) you want to become an expert in and take all the courses under that heading. You can also create your own custom subject; the Discord community may provide feedback on your planned subject.
Content policy. If you plan on showing off some of your coursework publicly, you must share only files that you are allowed to. Respect the code of conduct that you signed in the beginning of each course!
Getting help (Details about our FAQ and chatroom)
Community
- We have a Discord server! This should be your first stop to talk with other OSSU students. Why don't you introduce yourself right now? Join the OSSU Discord
- You can also interact through GitHub issues. If there is a problem with a course, or a change needs to be made to the curriculum, this is the place to start the conversation. Read more here.
- Add Open Source Society University to your Linkedin profile!
Warning: There are a few third-party/deprecated/outdated material that you might find when searching for OSSU. We recommend you to ignore them, and only use the OSSU CS website or OSSU CS Github Repo. Some known outdated materials are:
- An unmaintained and deprecated firebase app. Read more in the FAQ.
- An unmaintained and deprecated trello board
- Third-party notion templates
Curriculum
Curriculum version: 8.0.0
(see CHANGELOG)
Prerequisites
- Core CS assumes the student has already taken high school math, including algebra, geometry, and pre-calculus.
- Advanced CS assumes the student has already taken the entirety of Core CS and is knowledgeable enough now to decide which electives to take.
- Note that Advanced systems assumes the student has taken a basic physics course (e.g. AP Physics in high school).
Intro CS
Introduction to Programming
If you've never written a for-loop, or don't know what a string is in programming, start here. This course is self-paced, allowing you to adjust the number of hours you spend per week to meet your needs.
Topics covered:
simple programs
simple data structures
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Introduction to programming | 10 weeks | 10 hours/week | none | chat |
Introduction to Computer Science
This course will introduce you to the world of computer science. Students who have been introduced to programming, either from the courses above or through study elsewhere, should take this course for a flavor of the material to come. If you finish the course wanting more, Computer Science is likely for you!
Topics covered:
computation
imperative programming
basic data structures and algorithms
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Introduction to Computer Science and Programming using Python | 9 weeks | 15 hours/week | high school algebra | chat |
Core CS
All coursework under Core CS is required, unless otherwise indicated.
Core programming
Topics covered:
functional programming
design for testing
program requirements
common design patterns
unit testing
object-oriented design
static typing
dynamic typing
ML-family languages (via Standard ML)
Lisp-family languages (via Racket)
Ruby
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Systematic Program Design | 13 weeks | 8-10 hours/week | none | chat: part 1 / part 2 |
Class-based Program Design | 13 weeks | 5-10 hours/week | Systematic Program Design, High School Math | chat |
Programming Languages, Part A | 5 weeks | 4-8 hours/week | Systematic Program Design (Hear instructor) | chat |
Programming Languages, Part B | 3 weeks | 4-8 hours/week | Programming Languages, Part A | chat |
Programming Languages, Part C | 3 weeks | 4-8 hours/week | Programming Languages, Part B | chat |
Object-Oriented Design | 13 weeks | 5-10 hours/week | Class Based Program Design | chat |
Software Architecture | 4 weeks | 2-5 hours/week | Object Oriented Design | chat |
Core math
Discrete math (Math for CS) is a prerequisite and closely related to the study of algorithms and data structures. Calculus both prepares students for discrete math and helps students develop mathematical maturity.
Topics covered:
discrete mathematics
mathematical proofs
basic statistics
O-notation
discrete probability
and more
Courses | Duration | Effort | Notes | Prerequisites | Discussion |
---|---|---|---|---|---|
Calculus 1A: Differentiation (alternative) | 13 weeks | 6-10 hours/week | The alternate covers this and the following 2 courses | high school math | chat |
Calculus 1B: Integration | 13 weeks | 5-10 hours/week | - | Calculus 1A | chat |
Calculus 1C: Coordinate Systems & Infinite Series | 6 weeks | 5-10 hours/week | - | Calculus 1B | chat |
Mathematics for Computer Science (alternative) | 13 weeks | 5 hours/week | 2015/2019 solutions 2010 solutions 2005 solutions. | Calculus 1C | chat |
CS Tools
Understanding theory is important, but you will also be expected to create programs. There are a number of tools that are widely used to make that process easier. Learn them now to ease your future work writing programs.
Topics covered:
terminals and shell scripting
vim
command line environments
version control
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
The Missing Semester of Your CS Education | 2 weeks | 12 hours/week | - | chat |
Core systems
Topics covered:
procedural programming
manual memory management
boolean algebra
gate logic
memory
computer architecture
assembly
machine language
virtual machines
high-level languages
compilers
operating systems
network protocols
and more
Courses | Duration | Effort | Additional Text / Assignments | Prerequisites | Discussion |
---|---|---|---|---|---|
Build a Modern Computer from First Principles: From Nand to Tetris (alternative) | 6 weeks | 7-13 hours/week | - | C-like programming language | chat |
Build a Modern Computer from First Principles: Nand to Tetris Part II | 6 weeks | 12-18 hours/week | - | one of these programming languages, From Nand to Tetris Part I | chat |
Operating Systems: Three Easy Pieces | 10-12 weeks | 6-10 hours/week | - | Nand to Tetris Part II | chat |
Computer Networking: a Top-Down Approach | 8 weeks | 4–12 hours/week | Wireshark Labs | algebra, probability, basic CS | chat |
Core theory
Topics covered:
divide and conquer
sorting and searching
randomized algorithms
graph search
shortest paths
data structures
greedy algorithms
minimum spanning trees
dynamic programming
NP-completeness
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Divide and Conquer, Sorting and Searching, and Randomized Algorithms | 4 weeks | 4-8 hours/week | any programming language, Mathematics for Computer Science | chat |
Graph Search, Shortest Paths, and Data Structures | 4 weeks | 4-8 hours/week | Divide and Conquer, Sorting and Searching, and Randomized Algorithms | chat |
Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming | 4 weeks | 4-8 hours/week | Graph Search, Shortest Paths, and Data Structures | chat |
Shortest Paths Revisited, NP-Complete Problems and What To Do About Them | 4 weeks | 4-8 hours/week | Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming | chat |
Core security
Topics covered
Confidentiality, Integrity, Availability
Secure Design
Defensive Programming
Threats and Attacks
Network Security
Cryptography
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Cybersecurity Fundamentals | 8 weeks | 10-12 hours/week | - | chat |
Principles of Secure Coding | 4 weeks | 4 hours/week | - | chat |
Identifying Security Vulnerabilities | 4 weeks | 4 hours/week | - | chat |
Choose one of the following:
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Identifying Security Vulnerabilities in C/C++Programming | 4 weeks | 5 hours/week | - | chat |
Exploiting and Securing Vulnerabilities in Java Applications | 4 weeks | 5 hours/week | - | chat |
Core applications
Topics covered:
Agile methodology
REST
software specifications
refactoring
relational databases
transaction processing
data modeling
neural networks
supervised learning
unsupervised learning
OpenGL
ray tracing
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Databases: Modeling and Theory | 2 weeks | 10 hours/week | core programming | chat |
Databases: Relational Databases and SQL | 2 weeks | 10 hours/week | core programming | chat |
Databases: Semistructured Data | 2 weeks | 10 hours/week | core programming | chat |
Machine Learning | 11 weeks | 9 hours/week | Basic coding | chat |
Computer Graphics (alternative) | 6 weeks | 12 hours/week | C++ or Java, linear algebra | chat |
Software Engineering: Introduction | 6 weeks | 8-10 hours/week | Core Programming, and a sizable project | chat |
Core ethics
Topics covered:
Social Context
Analytical Tools
Professional Ethics
Intellectual Property
Privacy and Civil Liberties
and more
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Ethics, Technology and Engineering | 9 weeks | 2 hours/week | none | chat |
Introduction to Intellectual Property | 4 weeks | 2 hours/week | none | chat |
Data Privacy Fundamentals | 3 weeks | 3 hours/week | none | chat |
Advanced CS
After completing every required course in Core CS, students should choose a subset of courses from Advanced CS based on interest. Not every course from a subcategory needs to be taken. But students should take every course that is relevant to the field they intend to go into.
Advanced programming
Topics covered:
debugging theory and practice
goal-oriented programming
parallel computing
object-oriented analysis and design
UML
large-scale software architecture and design
and more
Courses | Duration | Effort | Prerequisites |
---|---|---|---|
Parallel Programming | 4 weeks | 6-8 hours/week | Scala programming |
Compilers | 9 weeks | 6-8 hours/week | none |
Introduction to Haskell | 14 weeks | - | - |
Learn Prolog Now! (alternative)* | 12 weeks | - | - |
Software Debugging | 8 weeks | 6 hours/week | Python, object-oriented programming |
Software Testing | 4 weeks | 6 hours/week | Python, programming experience |
(*) book by Blackburn, Bos, Striegnitz (compiled from source, redistributed under CC license)
Advanced systems
Topics covered:
digital signaling
combinational logic
CMOS technologies
sequential logic
finite state machines
processor instruction sets
caches
pipelining
virtualization
parallel processing
virtual memory
synchronization primitives
system call interface
and more
Courses | Duration | Effort | Prerequisites | Notes |
---|---|---|---|---|
Computation Structures 1: Digital Circuits alternative 1 alternative 2 | 10 weeks | 6 hours/week | Nand2Tetris II | Alternate links contain all 3 courses. |
Computation Structures 2: Computer Architecture | 10 weeks | 6 hours/week | Computation Structures 1 | |
Computation Structures 3: Computer Organization | 10 weeks | 6 hours/week | Computation Structures 2 |
Advanced theory
Topics covered:
formal languages
Turing machines
computability
event-driven concurrency
automata
distributed shared memory
consensus algorithms
state machine replication
computational geometry theory
propositional logic
relational logic
Herbrand logic
game trees
and more
Courses | Duration | Effort | Prerequisites |
---|---|---|---|
Theory of Computation (alternative) | 13 weeks | 10 hours/week | Mathematics for Computer Science, logic, algorithms |
Computational Geometry | 16 weeks | 8 hours/week | algorithms, C++ |
Game Theory | 8 weeks | 3 hours/week | mathematical thinking, probability, calculus |
Advanced Information Security
Courses | Duration | Effort | Prerequisites |
---|---|---|---|
Web Security Fundamentals | 5 weeks | 4-6 hours/week | understanding basic web technologies |
Security Governance & Compliance | 3 weeks | 3 hours/week | - |
Digital Forensics Concepts | 3 weeks | 2-3 hours/week | Core Security |
Secure Software Development: Requirements, Design, and Reuse | 7 weeks | 1-2 hours/week | Core Programming and Core Security |
Secure Software Development: Implementation | 7 weeks | 1-2 hours/week | Secure Software Development: Requirements, Design, and Reuse |
Secure Software Development: Verification and More Specialized Topics | 7 weeks | 1-2 hours/week | Secure Software Development: Implementation |
Advanced math
Courses | Duration | Effort | Prerequisites | Discussion |
---|---|---|---|---|
Essence of Linear Algebra | - | - | high school math | chat |
Linear Algebra | 14 weeks | 12 hours/week | corequisite: Essence of Linear Algebra | chat |
Introduction to Numerical Methods | 14 weeks | 12 hours/week | Linear Algebra | chat |
Introduction to Formal Logic | 10 weeks | 4-8 hours/week | Set Theory | chat |
Probability | 15 weeks | 5-10 hours/week | Differentiation and Integration | chat |
Final project
Part of learning is doing. The assignments and exams for each course are to prepare you to use your knowledge to solve real-world problems.
After you've completed Core CS and the parts of Advanced CS relevant to you, you should identify a problem that you can solve using the knowledge you've acquired. You can create something entirely new, or you can improve some tool/program that you use and wish were better.
Students who would like more guidance in creating a project may choose to use a series of project oriented courses. Here is a sample of options (many more are available, at this point you should be capable of identifying a series that is interesting and relevant to you):
Courses | Duration | Effort | Prerequisites |
---|---|---|---|
Fullstack Open | 12 weeks | 15 hours/week | programming |
Modern Robotics (Specialization) | 26 weeks | 2-5 hours/week | freshman-level physics, linear algebra, calculus, linear ordinary differential equations |
Data Mining (Specialization) | 30 weeks | 2-5 hours/week | machine learning |
Big Data (Specialization) | 30 weeks | 3-5 hours/week | none |
Internet of Things (Specialization) | 30 weeks | 1-5 hours/week | strong programming |
Cloud Computing (Specialization) | 30 weeks | 2-6 hours/week | C++ programming |
Data Science (Specialization) | 43 weeks | 1-6 hours/week | none |
Functional Programming in Scala (Specialization) | 29 weeks | 4-5 hours/week | One year programming experience |
Game Design and Development with Unity 2020 (Specialization) | 6 months | 5 hours/week | programming, interactive design |
Congratulations
After completing the requirements of the curriculum above, you will have completed the equivalent of a full bachelor's degree in Computer Science. Congratulations!
What is next for you? The possibilities are boundless and overlapping:
- Look for a job as a developer!
- Check out the readings for classic books you can read that will sharpen your skills and expand your knowledge.
- Join a local developer meetup (e.g. via meetup.com).
- Pay attention to emerging technologies in the world of software development:
- Explore the actor model through Elixir, a new functional programming language for the web based on the battle-tested Erlang Virtual Machine!
- Explore borrowing and lifetimes through Rust, a systems language which achieves memory- and thread-safety without a garbage collector!
- Explore dependent type systems through Idris, a new Haskell-inspired language with unprecedented support for type-driven development.
Code of conduct
How to show your progress
Fork the GitHub repo into your own GitHub account and put ✅ next to the stuff you've completed as you complete it. This can serve as your kanban board and will be faster to implement than any other solution (giving you time to spend on the courses).
Team
- Eric Douglas: founder of OSSU
- Josh Hanson: lead technical maintainer
- Waciuma Wanjohi: lead academic maintainer
- Contributors