This course covers elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.
This course covers elementary discrete mathematics for science and engineering, with a focus on mathematical tools and proof techniques useful in computer science. Topics include logical notation, sets, relations, elementary graph theory, state machines and invariants, induction and proofs by contradiction, recurrences, asymptotic notation, elementary analysis of algorithms, elementary number theory and cryptography, permutations and combinations, counting tools, and discrete probability.
The course provides a systematic framework to understand the most challenging issues in sustainability in the real estate industry. It examines economic mechanisms, technological advances, business models, building design, and investment and financing strategies available for the different market players to promote sustainability in the building sector. Prof. [Siqi Zheng](https://www.siqizheng.com/about) is the faculty director of the MIT Center for Real Estate and founder and director of the MIT Sustainable Urbanization Lab. She specializes in urban and environmental economics, with a special focus on sustainable cities and real estate. [Zhengzhen Tan](https://cre.mit.edu/people/zhengzhen-tan/) is a lecturer and researcher with MIT Center for Real Estate and MIT Asia Real Estate Initiative, specializing in real estate sustainability, healthy buildings, and digital technology innovation. Prof. [Juan Palacios](https://cre.mit.edu/people/juan-palacios/) is a visiting professor from Maastricht University whose research focuses on environmental economics, sustainable real estate, and health economics.
The course provides a systematic framework to understand the most challenging issues in sustainability in the real estate industry. It examines economic mechanisms, technological advances, business models, building design, and investment and financing strategies available for the different market players to promote sustainability in the building sector. Prof. [Siqi Zheng](https://www.siqizheng.com/about) is the faculty director of the MIT Center for Real Estate and founder and director of the MIT Sustainable Urbanization Lab. She specializes in urban and environmental economics, with a special focus on sustainable cities and real estate. [Zhengzhen Tan](https://cre.mit.edu/people/zhengzhen-tan/) is a lecturer and researcher with MIT Center for Real Estate and MIT Asia Real Estate Initiative, specializing in real estate sustainability, healthy buildings, and digital technology innovation. Prof. [Juan Palacios](https://cre.mit.edu/people/juan-palacios/) is a visiting professor from Maastricht University whose research focuses on environmental economics, sustainable real estate, and health economics.
Class 1, Part 1: Economic Growth Theory and the Direct Elements in Innovation 22:30まで
Class 1, Part 1: Economic Growth Theory and the Direct Elements in Innovation 9:00まで