Courses tagged with "Mathematics" (32)
The focus of the course is the concepts and techniques for solving the partial differential equations (PDE) that permeate various scientific disciplines. The emphasis is on nonlinear PDE. Applications include problems from fluid dynamics, electrical and mechanical engineering, materials science, quantum mechanics, etc.
This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.
This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. In addition, this course covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.
This course teaches a calculus that enables precise quantitative predictions of large combinatorial structures. Part I covers generating functions and real asymptotics and then introduces the symbolic method in the context of applications in the analysis of algorithms and basic structures such as permutations, trees, strings, words, and mappings.
Learn various methods of analysis including: unsupervised clustering, gene-set enrichment analyses, Bayesian integration, network visualization, and supervised machine learning applications to LINCS data and other relevant Big Data from high content molecular and phenotype profiling of human cells.
This is the second course in a two-part series on bioinformatics algorithms, covering the following topics: evolutionary tree reconstruction, applications of combinatorial pattern matching for read mapping, gene regulatory analysis, protein classification, computational proteomics, and computational aspects of human genetics.
This course teaches the concepts and computational methods in the exciting interdisciplinary field of bioinformatics and their applications in life sciences. The lectures are taught in both Mandarin Chinese and English with slides in English. 生物信息学是一门新兴的生命科学与计算科学的前沿交叉学科。本课程讲授生物信息学主要概念和方法，以及如何应用生物信息学手段解决生命科学问题。本课程同时提供中文普通话授课和英文授课两个版本，以及英文幻灯片。
Are you interested in learning how to program (in Python) within a scientific setting? This course will cover algorithms for solving various biological problems along with a handful of programming challenges helping you implement these algorithms in Python. It offers a gentler-paced alternative to the first course in our Bioinformatics Specialization (Finding Hidden Messages in DNA).
Understanding how the brain works is one of the fundamental challenges in science today. This course will introduce you to basic computational techniques for analyzing, modeling, and understanding the behavior of cells and circuits in the brain. You do not need to have any prior background in neuroscience to take this course.
This course introduces students to iterative decoding algorithms and the codes to which they are applied, including Turbo Codes, Low-Density Parity-Check Codes, and Serially-Concatenated Codes. The course will begin with an introduction to the fundamental problems of Coding Theory and their mathematical formulations. This will be followed by a study of Belief Propagation--the probabilistic heuristic which underlies iterative decoding algorithms. Belief Propagation will then be applied to the decoding of Turbo, LDPC, and Serially-Concatenated codes. The technical portion of the course will conclude with a study of tools for explaining and predicting the behavior of iterative decoding algorithms, including EXIT charts and Density Evolution.
This course introduces the basic computational methods used to understand the cell on a molecular level. It covers subjects such as the sequence alignment algorithms: dynamic programming, hashing, suffix trees, and Gibbs sampling. Furthermore, it focuses on computational approaches to: genetic and physical mapping; genome sequencing, assembly, and annotation; RNA expression and secondary structure; protein structure and folding; and molecular interactions and dynamics.