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Counting Principles

8 resources

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Type

🎓Courses(2)

course👁️ 0

Combinatorics and Probability

Counting is one of the basic mathematically related tasks we encounter on a day to day basis. The main question here is the following. If we need to count something, can we do anything better than just counting all objects one by one? Do we need to create a list of all phone numbers to ensure that there are enough phone numbers for everyone? Is there a way to tell that our algorithm will run in a reasonable time before implementing and actually running it? All these questions are addressed by a mathematical field called Combinatorics. In this online course we discuss most standard combinatorial settings that can help to answer questions of this type. We will especially concentrate on developing the ability to distinguish these settings in real life and algorithmic problems. This will help the learner to actually implement new knowledge. Apart from that we will discuss recursive technique for counting that is important for algorithmic implementations. One of the main ‘consumers’ of Combinatorics is Probability Theory. This area is connected with numerous sides of life, on one hand being an important concept in everyday life and on the other hand being an indispensable tool in such modern and important fields as Statistics and Machine Learning. In this course we will concentrate on providing the working knowledge of basics of probability and a good intuition in this area. The practice shows that such an intuition is not easy to develop. In the end of the course we will create a program that successfully plays a tricky and very counterintuitive dice game. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.

intermediate🇬🇧
course👁️ 0

Mathematics for Computer Science

Learn counting principles for computer science with this MIT course by Leighton & van Dijk. Master essential math skills!

advanced🇬🇧

🌐Websites(6)

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website👁️ 0

Brilliant.org Combinatorics

Interactive free lessons on counting (basic access free)

beginner🇬🇧
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Pauls Online Notes

Discrete Math section on counting techniques

beginner🇬🇧
website👁️ 0

Art of Problem Solving Wiki

Comprehensive free guide to counting principles with examples

beginner🇬🇧
website👁️ 0

mathworld.wolfram.com

MathWorld is an online mathematics encyclopedia by Wolfram that covers a wide range of topics, including combinatorics and counting principles. It features detailed articles with definitions, explanations, formulas, theorems, proofs, examples, diagrams, and extensive cross-links to related concepts.

intermediate🇬🇧
website👁️ 0

ocw.mit.edu

MIT OpenCourseWare (OCW) offers free, openly licensed MIT course materials—lectures, notes, assignments, and exams—for self-paced study across a wide range of subjects. It includes mathematics courses that cover topics like counting principles, with resources you can access directly online.

intermediate🇬🇧
website👁️ 0

khanacademy.org

Khan Academy is a free online learning platform offering self-paced math and other subjects with instructional videos, practice problems, and progress tracking. It covers counting principles, probability, and other foundational math topics through step-by-step tutorials and interactive exercises.

intermediate🇬🇧

Frequently Asked Questions

What are the best free resources to learn Counting Principles?

Dantes has curated 5 resources for Counting Principles, including 2 courses, 3 websites. All resources are hand-picked for quality — no algorithmic filler. Browse the full list above to find the format that works best for you.

Is Counting Principles hard to learn?

Counting Principles is approachable at the beginner level — there are resources here specifically for those starting from scratch. As you progress, intermediate and advanced material is also available to take your skills further.

What types of Counting Principles learning resources are available on Dantes?

For Counting Principles, Dantes has curated 2 courses, 3 websites. Each resource type serves a different learning style: videos and YouTube for visual learners, books for depth, courses for structured progression, and websites for quick reference.

How does Dantes select Counting Principles resources?

Dantes is an algorithm-free learning directory. Resources are hand-curated based on quality, accuracy, and usefulness — not engagement metrics or paid placements. The goal is to surface the best learning material for Counting Principles, whether it's a free YouTube series, a classic textbook, or an open courseware from a top university.

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