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MAT2580 Introduction to Linear Algebra

MAT2580 Introduction to Linear Algebra

Topics include systems of equations, matrices, determinants, eigenvalues and eigenvectors, inner products, vector spaces, and subspaces. Prereq: MAT1575 (Calculus II) Meeting Time – Mon/Wed: 1-2:15 p.m. Text: Linear Algebra and its Applications,4th Edition by David C. Lay. Publisher: Addison Wesley. Instructor’s name: Urmi Ghosh-Dastidar Office Hours: Mon: 11:50 – 12:50 p.m. Wed: 4:40 – 5:40 p.m. (Namm 726) Office: N726 ; Ph: (718)260-5349 Office: Pearl 616 (by appointment only) If you want to meet me other than the office hours please make an appointment. e-mail: ughosh-dastidar@citytech.cuny.edu Note: All exams will take place in-class unless stated otherwise. The final exam date and time is fixed. You have to make yourself available for all in-class exams and final exam Technology prerequisites: MATLAB will be used. In addition, a graphing calculator is required: We recommend a calculator which can compute eigenvalues. E-mail: All student must use City Tech e-mail address while taking this course. Reading e-mail on a regular basis is necessary. I may need to contact you via e-mail if situation arises. City Tech has provided all students with a City Tech email address. Your email address is the first letter of your first name, followed by your last name, followed by @campus.citytech.cuny.edu. You can access your email by going to the following web site: http://campus.citytech.cuny.edu/. For help with accessing email, you can also send an email to helpdesk@campus.citytech.cuny.edu. In case of emergency, you can call 718-254-8565 or email: epak@citytech.cuny.edu or rhoque@citytech.cuny.edu for technical help. Theme: Biodiversity: Eco-Math link through Linear Algebra A Brief Introduction Biodiversity and the Hudson River Flowing from the Lake Tear of the Clouds, North the Hudson River journeys 315 miles and drops 4,322 feet in elevation before emptying itself into New York Harbor. The Hudson River is home to diverse populations of fish, birds, and mammals that cohabit and compete among themselves for resources. Recently the American shad, Atlantic sturgeon, river herring (blue back herring and alewife), American eel, and largemouth bass are in decline. Intense economic harvesting pressure and overexploitation cause coastal and marine species to decline. Therefore, harvesting and fishing should be managed properly and carefully to avoid decline of current population. Food web analysis provides important information regarding the nature of competition among various organisms. Cluster analysis in graph theory is a popular method to seek partition of a given data set into several clusters so that the data points within the same cluster are more similar than those belonged in the separate clusters. In this project we will use cluster analysis using the concepts of linear algebra to study the competition among various species in a given food web, in particular, competition among various Hudson River species. Students will find a partition of the competition graphs based on the Hudson River food web such that the strength of competition (for shared preys) between two clusters (two groups of predators) is as low as possible; however, the strength of competition within the same clusters is as high as possible. Big Idea behind this project Study and analyze Hudson River Food Web and its competition graph to interpret the strength of species competition. Particularly we will be exploring the followings: • Which predator species are more connected than others? • What happens if a specific species (particularly, a prey) dies out? Particularly, how does the removal of a particular species affect its predators and also the overall competition among all predator species? I Students Learning Outcomes 1. To solve systems of linear equations using matrices. 2. To identify and use vector properties (spaces, subspaces, bases, inner product). 3. To identify properties of matrices (inevitability, eigenvalues, eigenvectors). 4. To use computer technology to solve problems. 5. To learn how to apply core mathematical concepts (particularly eigenvalues and eigenvectors) in solving real-world problems. 7. To understand interdisciplinary approach and the significance of it in real-world applications. General Education Learning Goals 1. To understand interdisciplinary approach and the significance of it in real-world applications. 2. To address a problem and resolve the problem with scientific methods.

2013 Fall – MAT 2070 Proofs and Logic – Reitz

2013 Fall – MAT 2070 Proofs and Logic – Reitz

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 and site header created using tagxedo.com.

MAT2572 Probability w/ Statistics, FA2016

MAT2572 Probability w/ Statistics, FA2016

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.

MEDU1010 Foundations of Math Ed, FA2013

MEDU1010 Foundations of Math Ed, FA2013

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.

ECON2505 Env Econ, FA2015

ECON2505 Env Econ, FA2015

This interdisciplinary course examines current environmental issues from a macroeconomic perspective, focusing on both the long and short-term economic viability of various proposals to address current environmental challenges. While the discipline of Economics serves as a central focus, the course draws extensively from the perspectives of Sociology, Architectural Technology, Environmental Control Technology, Hospitality Management (sustainable tourism), and Sustainable Technology. Traditional goals of economic efficiency will be examined in the context of the need to expand renewable energy sources, green building design and construction, sustainable agriculture and trade, resource allocation and other efforts to combat climate change on a global scale. It focuses on both the long and short-term economic viability of various proposals to address current environmental challenges drawing upon the inherent interdisciplinary connection to these vital economic issues.

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