This course is part of the Introduction to Discrete Mathematics for Computer Science Specialization

Offered By

University of California San Diego

National Research University Higher School of Economics

Introduction to Discrete Mathematics for Computer Science Specialization

University of California San Diego

About this Course

4.7

76 ratings

•

9 reviews

We’ll implement (in Python) together efficient programs for a problem needed by delivery companies all over the world millions times per day — the travelling salesman problem. The goal in this problem is to visit all the given places as quickly as possible. How to find an optimal solution to this problem quickly? We still don’t have provably efficient algorithms for this difficult computational problem and this is the essence of the P versus NP problem, the most important open question in Computer Science. Still, we’ll implement several solutions for real world instances of the travelling salesman problem. While designing these solutions, we will rely heavily on the material learned in the courses of the specialization: proof techniques, combinatorics, probability, graph theory. We’ll see several examples of using discrete mathematics ideas to get more and more efficient solutions.

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Suggested: 3 weeks of study, 2–5 hours/week...

Subtitles: English

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 3 weeks of study, 2–5 hours/week...

Subtitles: English

Week

1We start this module with the definition of mathematical model of the delivery problem — the classical traveling salesman problem (usually abbreviated as TSP). We'll then review just a few of its many applications: from straightforward ones (delivering goods, planning a trip) to less obvious ones (data storage and compression, genome assembly). After that, we will together take the first steps in implementing programs for TSP....

4 videos (Total 43 min), 1 reading, 4 quizzes

Shortest Common Superstring Problem10m

Brute Force Search11m

Nearest Neighbor8m

Additional Materials10m

Cycle Weight20m

Brute Force Algorithm2m

Average Weight30m

Nearest Neighbors2m

Week

2We'll see two general techniques applied to the traveling salesman problem. The first one, branch and bound, is a classical approach in combinatorial optimization that is used for various problems. It can be seen as an improvement of the brute force search: we try to construct a permutation piece by piece, but at each step we check whether it still makes sense to continue constructing the permutation (if it doesn't, we just cut off the current branch). The second one, dynamic programming, is arguably the most popular algorithmic technique. It solves a problem by going through a collection of smaller subproblems....

4 videos (Total 49 min), 2 quizzes

Dynamic Programming: Main Ideas9m

Dynamic Programming: Representing Subsets10m

Dynamic Programming: Code13m

Branch and Bounds

Dynamic Programmings

Week

3As we've seen in the previous modules, solving the traveling salesman problem exactly is hard. In fact, we don't even expect an efficient solution in the nearest future. For this reason, it makes sense to ask: is it possible to find efficiently a solution that is probably suboptimal, but at the same time is close to optimal? It turns out that the answer is yes! We'll learn two algorithms. The first one guarantees to find quickly a solution which is at most twice longer than the optimal one. The second algorithms does not have such guarantees, but it is known to work pretty well in practice....

2 videos (Total 20 min), 1 quiz

2-Approximation2m

4.7

9 ReviewsBy AS•Jul 25th 2018

This final course in 5 course specialization is relatively easy one, although the last problem takes little bit time to solve. Provides good introduction to difficult to learn Delivery problem.

By ES•Jun 19th 2018

perfect course! very easy and interesting to follow. Pseudo-Algorithms were very useful and helped a lot to understand the concepts.

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National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more.
Learn more on www.hse.ru...

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses....

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