Alexander S. Kulikov

 

 


 

Alexander S. Kulikov is a research fellow at St. Petersburg Department of Steklov Mathematical Institute of the Russian Academy of Sciences and a visiting professor at University of California, San Diego. His scientific interests include algorithms for NP-hard problems and circuit complexity. In St. Petersburg, he runs Computer Science Club and Computer Science Center.




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Sep 25th 2017

The course covers basic algorithmic techniques and ideas for computational problems arising frequently in practical applications: sorting and searching, divide and conquer, greedy algorithms, dynamic programming. We will learn a lot of theory: how to sort data and how it helps for searching; how to break a large problem into pieces and solve them recursively; when it makes sense to proceed greedily; how dynamic programming is used in genomic studies. You will practice solving computational problems, designing new algorithms, and implementing solutions efficiently (so that they run in less than a second).

Average: 7.6 (14 votes)
Sep 25th 2017

A good algorithm usually comes together with a set of good data structures that allow the algorithm to manipulate the data efficiently. In this course, we consider the common data structures that are used in various computational problems. You will learn how these data structures are implemented in different programming languages and will practice implementing them in our programming assignments.

Average: 8.1 (10 votes)
Sep 25th 2017

If you have ever used a navigation service to find optimal route and estimate time to destination, you've used algorithms on graphs. Graphs arise in various real-world situations as there are road networks, computer networks and, most recently, social networks! If you're looking for the fastest time to get to work, cheapest way to connect set of computers into a network or efficient algorithm to automatically find communities and opinion leaders in Facebook, you're going to work with graphs and algorithms on graphs.

Average: 7.3 (13 votes)

Sep 25th 2017

World and internet is full of textual information. We search for information using textual queries, we read websites, books, e-mails. All those are strings from the point of view of computer science. To make sense of all that information and make search efficient, search engines use many string algorithms. Moreover, the emerging field of personalized medicine uses many search algorithms to find disease-causing mutations in the human genome.

Average: 7.1 (13 votes)
Sep 25th 2017

You've learned the basic algorithms now and are ready to step into the area of more complex problems and algorithms to solve them. Advanced algorithms build upon basic ones and use new ideas. We will start with networks flows which are used in more obvious applications such as optimal matchings, finding disjoint paths and flight scheduling as well as more surprising ones like image segmentation in computer vision or finding dense clusters in the advertiser-search query graphs at search engines. We then proceed to linear programming with applications in optimizing budget allocation, portfolio optimization, finding the cheapest diet satisfying all requirements, call routing in telecommunications and many others. Next we discuss inherently hard problems for which no exact good solutions are known (and not likely to be found) and how to solve them approximately in a reasonable time. We finish with some applications to Big Data and Machine Learning which are heavy on algorithms right now.

Average: 6.6 (19 votes)
Sep 18th 2017

There is a perceived barrier to mathematics: proofs. In this course we will try to convince you that this barrier is more frightening than prohibitive: most proofs are easy to understand if explained correctly, and often they are even fun. We provide an accompanied excursion in the “proof zoo” showing you examples of techniques of different kind applied to different topics.

Average: 7 (1 vote)

Sep 18th 2017

We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the rigor of mathematics; is simple, but not unsophisticated. Graph Theory gives us, both an easy way to pictorially represent many major mathematical results, and insights into the deep theories behind them.

Average: 4.5 (4 votes)
Sep 18th 2017

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.

Average: 9 (1 vote)