This course teaches simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications are drawn from the physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis is on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world.

The Calculus I course was developed through the Ohio Department of Higher Education OER Innovation Grant. This work was completed and the course was posted in February 2019. The course is part of the Ohio Transfer Module and is also named TMM005. For more information about credit transfer between Ohio colleges and universities, please visit: www.ohiohighered.org/transfer.Team LeadJim Fowler                                         Ohio State UniversityRita Ralph                                         Columbus State Community CollegeContent ContributorsNela Lakos                                       Ohio State UniversityBart Snapp                                       Ohio State UniversityJames Talamo                                  Ohio State UniversityXiang Yan                                         Edison State Community CollegeLibrarianDaniel Dotson                                    Ohio State University                     Review TeamThomas Needham                             Ohio State UniversityCarl Stitz                                            Lakeland Community CollegeSara Rollo                                          North Central State College 

After completing this section, students should be able to do the following.Express the sum of n terms using sigma notation.Apply the properties of sums when working with sums in sigma notation.Understand the relationship between area under a curve and sums of areas of rectangles.Approximate area of the region under a curve.Compute left, right, and midpoint Riemann sums with 10 or fewer rectangles.Understand how Riemann sums with n rectangles are computed and how the exact value of the area is obtained by taking the limit as n→∞n→∞ .

The course focuses on the problem of supervised learning within the framework of Statistical Learning Theory. It starts with a review of classical statistical techniques, including Regularization Theory in RKHS for multivariate function approximation from sparse data. Next, VC theory is discussed in detail and used to justify classification and regression techniques such as Regularization Networks and Support Vector Machines. Selected topics such as boosting, feature selection and multiclass classification will complete the theory part of the course. During the course we will examine applications of several learning techniques in areas such as computer vision, computer graphics, database search and time-series analysis and prediction. We will briefly discuss implications of learning theories for how the brain may learn from experience, focusing on the neurobiology of object recognition. We plan to emphasize hands-on applications and exercises, paralleling the rapidly increasing practical uses of the techniques described in the subject.

Studies how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Models of randomized computation. Data structures: hash tables, and skip lists. Graph algorithms: minimum spanning trees, shortest paths, and minimum cuts. Geometric algorithms: convex hulls, linear programming in fixed or arbitrary dimension. Approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.