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Courseware
The course is taught using the textbook by T. Apostol, "Calculus" Vol. I Second Edition (1967) and the additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Mathematical analysis
- Resource Type:
- Courseware
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Courseware
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Differential equations
- Resource Type:
- Courseware
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Courseware
This course aims to give students the tools and training to recognize convex optimization problems that arise in scientific and engineering applications, presenting the basic theory, and concentrating on modeling aspects and results that are useful in applications. Topics include convex sets, convex functions, optimization problems, least-squares, linear and quadratic programs, semidefinite programming, optimality conditions, and duality theory. Applications to signal processing, control, machine learning, finance, digital and analog circuit design, computational geometry, statistics, and mechanical engineering are presented. Students complete hands-on exercises using high-level numerical software.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Convex functions Mathematical optimization
- Resource Type:
- Courseware
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Video
Engineering Mathematics tutorial series covers aspects of applied mathematics including: multivariable calculus; vector field theory; differential equations; Laplace transforms and Fourier series.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Engineering mathematics
- Resource Type:
- Video
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Others
Euclid’s Elements was a collection of 13 books about geometry originally written circa 300 BC. Shortly after the advent of the printing press, many editions and translations have been created over the centuries. Byrne’s 1847 edition of the first six books stands out for its unique use of colorful illustrations to demonstrate proofs rather than using letters to label angles, edges, and shapes. His edition was one of the first books to be published with such detailed use of colors and combined with its detailed diagrams makes it an impressive feat of publishing for the times and it stands out even today as a work of art. This site is a reproduction of Byrne’s Euclid by Oliver Byrne from 1847 that pays tribute to the beautiful original design and includes enhancements such as interactive diagrams, cross references, and posters designed by Nicholas Rougeux.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Euclid's Elements Elements (Euclid) Geometry
- Resource Type:
- Others
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MOOC
This course teaches the R programming language in the context of statistical data and statistical analysis in the life sciences. We will learn the basics of statistical inference in order to understand and compute p-values and confidence intervals, all while analyzing data with R code. We provide R programming examples in a way that will help make the connection between concepts and implementation. Problem sets requiring R programming will be used to test understanding and ability to implement basic data analyses. We will use visualization techniques to explore new data sets and determine the most appropriate approach. We will describe robust statistical techniques as alternatives when data do not fit assumptions required by the standard approaches. By using R scripts to analyze data, you will learn the basics of conducting reproducible research. Given the diversity in educational background of our students we have divided the course materials into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. We start with simple calculations and descriptive statistics. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.
- Subjects:
- Statistics and Research Methods and Mathematics and Statistics
- Keywords:
- Life sciences -- Statistical methods Mathematical statistics -- Data processing R (Computer program language)
- Resource Type:
- MOOC
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MOOC
This course covers a wide variety of topics in machine learning and statistical modeling. While mathematical methods and theoretical aspects will be covered, the primary goal is to provide students with the tools and principles needed to solve the data science problems found in practice. This course also serves as a foundation on which more specialized courses and further independent study can build. This course was designed as part of the core curriculum for the Center for Data Science's Masters degree in Data Science. Other interested students who satisfy the prerequisites are welcome to take the class as well. Note that class is intended as a continuation of DS-GA-1001 Intro to Data Science, which covers some important, fundamental data science topics that may not be explicitly covered in this DS-GA class (e.g. data cleaning, cross-validation, and sampling bias).
- Course related:
- LGT6801 Guided Study in Logistics I
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Big data Data mining Machine learning Mathematical statistics -- Data processing
- Resource Type:
- MOOC
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Others
Math explained in easy language, plus puzzles, games, worksheets and an illustrated dictionary.
- Course related:
- AMA1110 Basic Mathematics I – Calculus and Probability & Statistics and AMA1120 Basic Mathematics II – Calculus and Linear Algebra
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics
- Resource Type:
- Others
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Others
Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration). All common integration techniques and even special functions are supported. The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions.
- Course related:
- AMA1120 Basic Mathematics II - Calculas and Linear Algebra
- Subjects:
- Mathematics and Statistics
- Keywords:
- Calculus Integral
- Resource Type:
- Others
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Video
Statistics, Machine Learning and Data Science can sometimes seem like very scary topics, but since each technique is really just a combination of small and simple steps, they are actually quite simple. My goal with StatQuest is to break down the major methodologies into easy to understand pieces. That said, I don't dumb down the material. Instead, I build up your understanding so that you are smarter.
- Course related:
- HTI34016 Introduction to Clinical Research
- Subjects:
- Computing and Mathematics and Statistics
- Keywords:
- Statistics Mathematical analysis Data mining Machine learning
- Resource Type:
- Video