The Financial Algebra Course engages students with real-world financial applications while maintaining deep mathematical rigor. The 10 units include: Taxes, Checking, Savings, Budgeting, Intro to Investing, Investing Strategies, Types of Credit, Managing Credit, Paying for College and Insurance.

This course will be heavily collaboration and project based. Students will be required to use google drive, docs and sheets on a regular basis. This course has a distinction of Algebra 1/Integrated 1 or higher. This is a good course for 11th and 12th grade students as an alternative to Integrated 3/Algebra 2.

This course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results.

This course presents finite element theory and methods for general linear and nonlinear analyses. Reliable and effective finite element procedures are discussed with their applications to the solution of general problems in solid, structural, and fluid mechanics, heat and mass transfer, and fluid-structure interactions. The governing continuum mechanics equations, conservation laws, virtual work, and variational principles are used to establish effective finite element discretizations and the stability, accuracy, and convergence are discussed. The homework and the student-selected term project using the general-purpose finite element analysis program ADINA are important parts of the course.

Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses.
These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study.

In this activity, students will model a noisy set of bacterial cell count data using both exponential and logistic growth models. For each model the students will plot the data (or a linear transformation of the data) and apply the method of least squares to fit the model's parameters. Activities include both theoretical and conceptual work, exploring the properties of the differential equation models, as well as hands-on computational work, using spreadsheets to quickly process large amounts of data. This activity is meant as a capstone to the differential calculus portion of a typical undergraduate Calculus I course. It explores a biological application of a variety of differential calculus concepts, including: differential equations, numerical differentiation, optimization, and limits. Additional topics explored include semi-log plots and linear regression.

Inspired by the work of the architect Antoni Gaudi, this research workshop will explore three-dimensional problems in the static equilibrium of structural systems. Through an interdisciplinary collaboration between computer science and architecture, we will develop design tools for determining the form of three-dimensional structural systems under a variety of loads. The goal of the workshop is to develop real-time design and analysis tools which will be useful to architects and engineers in the form-finding of efficient three-dimensional structural systems.

This subject describes and illustrates computational approaches to solving problems in systems biology. A series of case-studies will be explored that demonstrate how an effective match between the statement of a biological problem and the selection of an appropriate algorithm or computational technique can lead to fundamental advances. The subject will cover several discrete and numerical algorithms used in simulation, feature extraction, and optimization for molecular, network, and systems models in biology.

This course is an introduction to computational biology emphasizing the fundamentals of nucleic acid and protein sequence and structural analysis; it also includes an introduction to the analysis of complex biological systems. Topics covered in the course include principles and methods used for sequence alignment, motif finding, structural modeling, structure prediction and network modeling, as well as currently emerging research areas.

In this course, you will cover some of the most basic math applications, like decimals, percents, and even fractions. You will not only learn the theory behind these topics, but also how to apply these concepts to your life. You will learn some basic mathematical properties, such as the reflexive property, associative property, and others. The best part is that you most likely already know them, even if you did not know the proper mathematical terminology.

This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals.

This class provides an introduction to quantitative models and qualitative frameworks for studying complex engineering systems. Also taught is the art of abstracting a complex system into a model for purposes of analysis and design while dealing with complexity, emergent behavior, stochasticity, non-linearities and the requirements of many stakeholders with divergent objectives. The successful completion of the class requires a semester-long class project that deals with critical contemporary issues which require an integrative, interdisciplinary approach using the above models and frameworks.

The objective of this course is to introduce large-scale atomistic modeling techniques and highlight its importance for solving problems in modern engineering sciences. We demonstrate how atomistic modeling can be used to understand how materials fail under extreme loading, involving unfolding of proteins and propagation of cracks.
This course was featured in an MIT Tech Talk article.

As taught in 2006-2007 and 2007-2008.

Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions.

This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include:

– norm topology and topological isomorphism;
– boundedness of operators;
– compactness and finite dimensionality;
– extension of functionals;
– weak*-compactness;
– sequence spaces and duality;
– basic properties of Banach algebras.

Suitable for: Undergraduate students Level Four

Dr Joel F. Feinstein
School of Mathematical Sciences

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.

This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted.
This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.

Introductory Statistics Course covering hypothesis testing, confidence interval, sampling, probability, counting techniques, correlation, linear regression, data collection and more.

This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, and limit theorems. There is also a number of additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; and deeper understanding of conditional distributions and expectations.

Quantum information is the foundation of the second quantum revolution. With classical computers and the classical internet, we are always manipulating classical information, made of bits. On the other hand, quantum computing and quantum communication consist in the processing of quantum information, made of qubits.

Take away the hardware, and all quantum computers work the same way, through the clever manipulation of quantum information and entanglement. This course provides a deeper understanding of some of the topics covered in our Quantum 101 program, namely, the representation and manipulation of quantum information at the level of abstract quantum circuits. Specifically, single and multi-qubit gates and circuits are introduced, and basic algorithms and protocols such as quantum state teleportation, superdense coding, and entanglement swapping are discussed. The course also presents quantum gate sets, their universality, and compilations between different gate expressions. These concepts are then made concrete with the Quantum Inspire simulator (a cloud-based quantum computing platform, created and maintained by QuTech at TU Delft), and the physics and operations with spin qubits will be detailed. The course concludes with an examination of quantum supremacy and near-term quantum devices, also known as "noisy-intermediate scale" (NISQ) quantum computing.

The course is a journey of discovery, so we encourage you to bring your own experiences, insights and thoughts to discuss on the forum!

This course is authored by experts from the QuTech research center at Delft University of Technology. In the center, scientists and engineers work together to drive research and development in quantum technology. QuTech Academy's aim is to inspire, share and disseminate knowledge about the latest developments in quantum technology.

This course provides a rigorous treatment of non-cooperative solution concepts in game theory, including rationalizability and Nash, sequential, and stable equilibria. It covers topics such as epistemic foundations, higher order beliefs, bargaining, repeated games, reputation, supermodular games, and global games. It also introduces cooperative solution concepts—Nash bargaining solution, core, Shapley value—and develops corresponding non-cooperative foundations.

This course introduces students to the rudiments of game theory as practiced in political science. It teaches students the basic elements of formal modeling and strategies for solving simple games. Readings draw from introductory texts on game theoretic modeling and applied articles in American politics, international relations, and comparative politics.