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The course PHYS 3100 of­fers a study of clas­si­cal me­chan­ics from a more ad­vanced per­spec­tive than fresh­man physics, with par­tic­u­lar em­pha­sis on La­grangian and Hamil­ton­ian for­malisms. Top­ics in­clude a re­view of New­ton­ian me­chan­ics and the prin­ci­ples of con­ser­va­tion of en­ergy and mo­men­tum, as well as the study of the cal­cu­lus of vari­a­tions, La­grange’ s equa­tions, two bod­ies cen­tral force prob­lems, me­chan­ics in non-in­er­tial frames, rigid bod­ies, Hamil­ton­ian me­chan­ics, col­li­sion the­ory.

The course PHYS 3100 offers a study of classical mechanics from a more advanced perspective than freshman physics, with particular emphasis on Lagrangian and Hamiltonian formalisms. Topics include a review of Newtonian mechanics and the principles of conservation of energy and momentum, as well as the study of the calculus of variations, Lagrange’ s equations, two bodies central force problems, mechanics in non-inertial frames, rigid bodies, Hamiltonian mechanics, collision theory.

Prepa­ra­tion for teach­ing an ad­vanced math­e­mat­ics cur­ricu­lum with a focus on the processes of math­e­mat­i­cal ar­gu­men­ta­tion and rea­son­ing, de­duc­tion, and dis­cov­ery. Top­ics in­clude propo­si­tional and firstorder logic, ax­iomatic ap­proach to num­ber the­ory, set the­ory and ab­stract prop­er­ties of re­la­tions, with a par­tic­u­lar em­pha­sis on num­ber the­ory.

Preparation for teaching an advanced mathematics curriculum with a focus on the processes of mathematical argumentation and reasoning, deduction, and discovery. Topics include propositional and firstorder logic, axiomatic approach to number theory, set theory and abstract properties of relations, with a particular emphasis on number theory.

Fun­da­men­tal eco­nomic ideas and the op­er­a­tion of the econ­omy on a na­tional scale. Pro­duc­tion dis­tri­b­u­tion and con­sump­tion of goods and ser­vices, the ex­change process, the role of gov­ern­ment, the na­tional in­come and its dis­tri­b­u­tion, GDP, con­sump­tion func­tion, sav­ings func­tion, in­vest­ment spend­ing, the mul­ti­plier prin­ci­ple and the in­flu­ence of gov­ern­ment spend­ing on in­come and out­put. Analy­sis of mon­e­tary pol­icy, in­clud­ing the bank­ing sys­tem and the Fed­eral Re­serve Sys­tem.

Fundamental economic ideas and the operation of the economy on a national scale. Production distribution and consumption of goods and services, the exchange process, the role of government, the national income and its distribution, GDP, consumption function, savings function, investment spending, the multiplier principle and the influence of government spending on income and output. Analysis of monetary policy, including the banking system and the Federal Reserve System.

A pro­ject-based in­tro­duc­tion to com­pu­ta­tional think­ing and prob­lem solv­ing. Cov­ers a wide range of top­ics, in­clud­ing data vi­su­al­iza­tion, sta­tis­ti­cal tech­niques, sim­u­la­tions of dy­nam­i­cal sys­tems, com­pu­ta­tional tech­niques to un­der­stand data, using re­gres­sion to fit mod­els to data, as well as an in­tro­duc­tion to some more ad­vanced top­ics: Monte Carlo sim­u­la­tions, op­ti­miza­tion, dy­namic pro­gram­ming, image pro­cess­ing, nat­ural lan­guage pro­cess­ing, geospa­tial data analy­sis and cur­rent data sci­ence.

A project-based introduction to computational thinking and problem solving. Covers a wide range of topics, including data visualization, statistical techniques, simulations of dynamical systems, computational techniques to understand data, using regression to fit models to data, as well as an introduction to some more advanced topics: Monte Carlo simulations, optimization, dynamic programming, image processing, natural language processing, geospatial data analysis and current data science.

Cal­cu­lus I

Calculus I