Introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory and optimization techniques. Emphasis on basic ideas and on applications in mechanical engineering. Selection will change every year. This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

This course focuses on the problem of supervised learning from the perspective of modern statistical learning theory starting with the theory of multivariate function approximation from sparse data. It develops basic tools such as Regularization including Support Vector Machines for regression and classification. It derives generalization bounds using both stability and VC theory. It also discusses topics such as boosting and feature selection and examines applications in several areas: Computer Vision, Computer Graphics, Text Classification and Bioinformatics. The final projects and hands-on applications and exercises are planned, paralleling the rapidly increasing practical uses of the techniques described in the subject.

Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.

This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes.

This course is an introduction to statistical data analysis. Topics are chosen from applied probability, sampling, estimation, hypothesis testing, linear regression, analysis of variance, categorical data analysis, and nonparametric statistics.

A whirl-wind tour of the statistics used in behavioral science research, covering topics including: data visualization, building your own null-hypothesis distribution through permutation, useful parametric distributions, the generalized linear model, and model-based analyses more generally. Familiarity with MATLABA, Octave, or R will be useful, prior experience with statistics will be helpful but is not essential. This course is intended to be a ground-up sketch of a coherent, alternative perspective to the "null-hypothesis significance testing" method for behavioral research (but don't worry if you don't know what this means).

This course is a broad treatment of statistics, concentrating on specific statistical techniques used in science and industry. Topics include: hypothesis testing and estimation, confidence intervals, chi-square tests, nonparametric statistics, analysis of variance, regression, correlation, decision theory, and Bayesian statistics.

This module is about a particular effect of the frequency, which is the stroboscopic effect. The lesson discusses and demonstrates low frequency phenomena - less than 16 Hz - that can usually be observed clearly by the human eye, as well as high frequency phenomena - more than 25 Hz - that are difficult for the human eye to catch. This video also explores and demonstrates how high frequency phenomena can be observed by freezing the fast moving phenomena using a device called a stroboscope. The only prerequisite for this video is that students understand the definition of the frequency of a periodic phenomenon.

The main objective of this video lesson is to bring the students' attention to the importance of basic and natural sciences in our lives. The lesson will introduce a topic (sustainable energy) that is related mainly to chemistry and is not usually covered directly in a high school curriculum. We hope that this lesson will show students how important and useful the natural and basic sciences are not only for our daily lives, but also for sustainable development. The lesson will present creative and challenging ideas on the topic of alternative energies. It is hoped that students will be inspired by the introduction of these ideas, and that they will develop the confidence to come up with creative ideas themselves. Background for this lesson is based on fundamental concepts in chemistry (mainly), biology, physics and environmental science.

This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.

This learning video presents an introduction to graph theory through two fun, puzzle-like problems: ''The Seven Bridges of Konigsberg'' and ''The Chinese Postman Problem''. Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem.

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.   

This course covers topics such as sums of independent random variables, central limit phenomena, infinitely divisible laws, Levy processes, Brownian motion, conditioning, and martingales.

This lesson is an introductory topic in thermodynamics, on the conversion of energy. The aim of this video is to support students in visualizing the conversion of energy and its importance in real world applications. For this reason, everyday examples are used to help students see the conversion of energy around them. Energy conversion is explored through a simple example of generating electricity for lighting up a shadow puppetry play in a village. The chain process of energy conversion is illustrated until the end product of electricity. This example of electricity generation is further illustrated in an actual industrial setting by taking the viewers to a Power Plant, where viewers will see and hear the explanation of a mechanical engineer on the equipment used to produce electricity that we use in homes and businesses. This important concept of energy conversion is crucial for students to understand as a basis for learning other concepts in Thermodynamics.

The course provides a survey of the theory and application of time series methods in econometrics.

The course provides a survey of the theory and application of time series methods in econometrics.

How is it that all cells in our body have the same genes, yet cells in different tissues express different genes? A basic notion in biology that most high school students fail to conceptualize is the fact that all cells in the animal or human body contain the same DNA, yet different cells in different tissues express, on the one hand, a set of common genes, and on the other, express another set of genes that vary depending on the type of tissue and the stage of development. In this video lesson, the student will be reminded that genes in a cell/tissue are expressed when certain conditions in the nucleus are met. Interestingly, the system utilized by the cell to ensure tissue specific gene expression is rather simple. Among other factors - all discussed fully in the lesson - the cells make use of a tiny scaffold known as the “Nuclear Matrix or Nucleo-Skeleton”. This video lesson spans 20 minutes and provides 5 exercises for students to work out in groups and in consultation with their classroom teacher. The entire duration of the video demonstration and exercises should take about 45-50 minutes, or equivalent to one classroom session. There are no supplies needed for students’ participation in the provided exercises. They will only need their notebooks and pens. However, the teacher may wish to emulate the demonstrations used in the video lesson by the presenter and in this case simple material can be used as those used in the video. These include play dough, pencils, rubber bands (to construct the nuclear matrix model), a tennis ball and 2-3 Meters worth of shoe laces. The students should be aware of basic information about DNA folding in the nucleus, DNA replication, gene transcription, translation and protein synthesis.

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.