Mathematical Biology
These are my lecture notes for a course I teach on mathematical biology at the Hong Kong University of Science & Technology. My main emphasis is on mathematical modeling, with biology the sole application area.
Probability
Definition of “probability” and examples.
Basic Analysis: Introduction to Real Analysis
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course woul
Multivariable Calculus
This is a textbook for a course in multivariable calculus that has been used for the past few years at Georgia Tech.
Complex Analysis
This is a textbook for an introductory course in complex analysis. It has been used for the undergraduate complex analysis course at Georgia Tech and at a few other places.
Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis
Introduction to Vectors and Tensors, Vol. 2, Vector and Tensor Analysis is a typed revision of the book originally published by Plenum Press in 1976 as Volume 2 in their series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.
Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra
Introduction to Vectors and Tensors, Vol. 1, Linear and Multilinear Algebra is a typed revision that was originally published by Plenum Press in 1976 as Volume 1 in a series on Mathematical Concepts and Methods in Science and Engineering, edited by Angelo Miele. PDF File.
Searching for Protoplanetary Disks
Students will download NASA Hubble Space Telescope views of star-forming regions in nebulae and look for evidence of planetary systems forming beyond our own solar system.
The Shapes of Our World. Experimenting With the Language of Geometry
In this lesson, students play a game of charades as an experiment in non-verbal communication. They then create maps with directions that demonstrate their ability to utilize shapes and spatial relationships in a practical context. Their learning is culminated in a written critical essay about the universality of human understanding.
Teach Your Parents Well - Educating Adults to Help Bridge the Digital Divide
In this lesson, students will consider the information they know that their parents don’t regarding today’s technology and popular culture. To help bridge the divide, students develop course outlines and lesson plans designed to teach adults what they need to know to keep in step with today’s youth.
Suffer the Little Children - Reflecting on Child Labor in Guatemala
In this lesson, students learn about and respond to the plight of child workers in Guatemala in the face of increased free trade through the Central American Free Trade Agreement.
Proving (a Theorem) and Disproving (a Theory). Applying the Pythagorean Theorem to Real Life
In this lesson, students share thoughts about careers and gender roles. They then work together to prepare a proof of the Pythagorean theorem and synthesize their learning by preparing a creative representation of Pythagoras' ideas.
Living on the Grid - Playing and Deconstructing Logic Games
In this lesson, students play and deconstruct the mathematical and strategic principles of logic puzzles, including tic-tac-toe and sudoku, as well as new games like kakuro, masyu, and nurikabe. They then prepare strategies for a user's guide to one game.
Invention Convention - Inventing and Marketing Products to Make Life Easier
In this lesson, students work in groups to create products that can help address everyday annoyances. They then design business plans for the manufacturing and marketing of their inventions.
Here Comes the . . . Bill. Preparing a Budget for a Milestone Event
In this lesson, students share opinions about the importance of milestone events they might host or attend. They then prepare estimated budgets for parties based on established budget totals, and compare their estimates against the real costs.
Graphic Accounts - Analyzing Graphs in The New York Times
In this lesson, students learn about the estimated cost of the war in Iraq to the U.S. government in comparison to other hypothetical expenditures, in part by examining a bar graph. They then explore the use of different types of graphs in The New York Times.
Don't Bet the House On It! Examining Mortgages through Real Estate Simulations
In this lesson, students will determine how much different families can afford to spend on real estate by taking on personas and creating budgets.
All About Aid-Navigating the World of Student Loans
In this lesson, students create presentations for graduating seniors about how to navigate the college financial aid system.
6.047 Computational Biology: Genomes, Networks, Evolution (MIT)
This course focuses on the algorithmic and machine learning foundations of computational biology, combining theory with practice. We study the principles of algorithm design for biological datasets, and analyze influential problems and techniques. We use these to analyze real datasets from large-scale studies in genomics and proteomics. The topics covered include:
Genomes: biological sequence analysis, hidden Markov models, gene finding, RNA folding, sequence alignment, genome assembly
Networks
