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This course is de­signed to pre­pare stu­dents for an ad­vanced math­e­mat­ics cur­ricu­lum by pro­vid­ing a tran­si­tion from Cal­cu­lus to ab­stract math­e­mat­ics. The course fo­cuses on the processes of math­e­mat­i­cal rea­son­ing, ar­gu­ment, and dis­cov­ery. Top­ics in­clude propo­si­tional and first order logic, learn­ing proofs through puz­zles and games, ax­iomatic ap­proach to group the­ory, num­ber the­ory, and set the­ory, ab­stract prop­er­ties of re­la­tions and func­tions, el­e­men­tary graph the­ory, sets of dif­fer­ent car­di­nal­i­ties, and the con­struc­tion and prop­er­ties of real num­bers. Avatar by flickr user bet­tys­nake: https://​www.​flickr.​com/​photos/​bettysnake/​65497164 Header image by flickr user thei­hno: https://​www.​flickr.​com/​photos/​theihno/​4156207919

This course is designed to prepare students for an advanced mathematics curriculum by providing a transition from Calculus to abstract mathematics. The course focuses on the processes of mathematical reasoning, argument, and discovery. Topics include propositional and first order logic, learning proofs through puzzles and games, axiomatic approach to group theory, number theory, and set theory, abstract properties of relations and functions, elementary graph theory, sets of different cardinalities, and the construction and properties of real numbers. Avatar by flickr user bettysnake: https://www.flickr.com/photos/bettysnake/65497164 Header image by flickr user theihno: https://www.flickr.com/photos/theihno/4156207919

This course ex­am­ines the his­tor­i­cal, philo­soph­i­cal, and so­ci­o­log­i­cal foun­da­tions un­der­ly­ing the de­vel­op­ment of Amer­i­can ed­u­ca­tional in­sti­tu­tions. The role of the schools, the aims of ed­u­ca­tion, di­verse learn­ers, the math­e­mat­ics cur­ricu­lum in New York State, legal prin­ci­ples that af­fect ed­u­ca­tion, and the role of state, local, and fed­eral agen­cies will be em­pha­sized.

This course examines the historical, philosophical, and sociological foundations underlying the development of American educational institutions. The role of the schools, the aims of education, diverse learners, the mathematics curriculum in New York State, legal principles that affect education, and the role of state, local, and federal agencies will be emphasized.

Top­ics for the course in­clude sam­ple spaces and prob­a­bil­i­ties, dis­crete dis­tri­b­u­tions (Bi­no­mial, Neg­a­tive Bi­no­mial, Geo­met­ric, Hy­per­ge­o­met­ric, Pois­son, and Gamma), con­tin­u­ous dis­tri­b­u­tions (Uni­form, Nor­mal, Chi-squared), ex­pec­ta­tion and vari­ance, hy­poth­e­sis test­ing, in­ter­val es­ti­ma­tion and con­fi­dence in­ter­vals. There will be ex­ten­sive use of MS Excel and R, a sta­tis­ti­cal soft­ware pro­gram. At the end of the course, stu­dents should be able make mean­ing­ful con­nec­tions be­tween sta­tis­tics and other areas of study, in­clud­ing and so­cial sci­ences.

Topics for the course include sample spaces and probabilities, discrete distributions (Binomial, Negative Binomial, Geometric, Hypergeometric, Poisson, and Gamma), continuous distributions (Uniform, Normal, Chi-squared), expectation and variance, hypothesis testing, interval estimation and confidence intervals. There will be extensive use of MS Excel and R, a statistical software program. At the end of the course, students should be able make meaningful connections between statistics and other areas of study, including and social sciences.

This course is an in­tro­duc­tion to num­ber the­ory. Top­ics in­clude di­vis­i­bil­ity (di­vi­sion al­go­rithm, GCD, etc), primes, con­gru­ence, the fun­da­men­tal the­o­rem of arith­metic, qua­dratic rec­i­proc­ity, num­ber the­o­retic func­tions and Fer­mat’s lit­tle the­o­rem. Some ap­pli­ca­tions will be done, which can be com­puter based, to en­cour­age stu­dents to pro­pose and test con­jec­tures. Avatar taken from https://​www.​atm.​org.​uk/​Association-​of-​Teachers-​of-​Mathematics Header taken from https://​www.​win.​tue.​nl/~bdeweger/getalthe­o­rie.html

This course is an introduction to number theory. Topics include divisibility (division algorithm, GCD, etc), primes, congruence, the fundamental theorem of arithmetic, quadratic reciprocity, number theoretic functions and Fermat’s little theorem. Some applications will be done, which can be computer based, to encourage students to propose and test conjectures. Avatar taken from https://www.atm.org.uk/Association-of-Teachers-of-Mathematics Header taken from https://www.win.tue.nl/~bdeweger/getaltheorie.html

A Learn­ing com­mu­nity be­tween MEDU 2010 and MEDU 3011.

A Learning community between MEDU 2010 and MEDU 3011.