Animals, Architecture, and Innovation.
This course provides a brisk, entertaining treatment of differential and integral calculus, with an emphasis on conceptual understanding and applications to the engineering, physical, and social sciences.
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences.Distinguishing features of the course include:
- the introduction and use of Taylor series and approximations from the beginning;
- a novel synthesis of discrete and continuous forms of Calculus;
- an emphasis on the conceptual over the computational; and
- a clear, dynamic, unified approach.
Animals, Architecture, and Innovation.
Statistics is about extracting meaning from data. In this class, we will introduce techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics.
This tutorial covers several mathematical techniques that are frequently used in complex systems science. The techniques are covered in independent units, taught by different instructors. Each unit has its own prerequisites. Note that this tutorial is meant to introduce students to various important techniques and to provide illustrations of their application in complex systems. A given unit is not meant to offer complete coverage of its topic or substitute for an entire course on that topic.
Numerical methods have been used to solve mathematical expressions of engineering and scientific problems for at least 4000 years. Such methods apply numerical approximation in order to convert continuous mathematical problems (for example, determining the mechanical stress throughout a loaded truss) into systems of discrete equations that can be solved with sufficient accuracy by machine. This course will provide you with an introduction to several of those numerical methods which you may then find opportunity to practice later in the curriculum.
This course follows on from FE & RM Part I. We will consider portfolio optimization, risk management and some advanced examples of derivatives pricing that draw from structured credit, real options and energy derivatives. We will also cast a critical eye on how financial models are used in practice.
This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling.
In this course, you will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge.
Entering university or college soon? Planning on taking some mathematics classes there--perhaps for your program in engineering, science or business? If you want a refresher on the most important terminology and notation for first year university mathematics, then this short course is just for you. The course will be especially useful if you are from a non-English speaking background.
Multivariable Calculus is an expansion of Single-Variable Calculus in that it extends single variable calculus to higher dimensions. You may find that these courses share many of the same basic concepts, and that Multivariable Calculus will simply extend your knowledge of functions to functions of several variables.
A matemática é a ciência do raciocínio lógico e abstrato, estuda quantidades, medidas, espaços, estruturas e variações. Um trabalho matemático consiste em procurar por padrões, formular conjecturas e, por meio de deduções rigorosas a partir de axiomas e definições, estabelecer novos resultados.