Apply tools of single-variable calculus to create and analyze mathematical models used by real practitioners in social, life, and physical sciences. In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work....

学习使用数学建模的方法并通过定量和定性分析模型更好地理解生物现象。Learn to use mathematical models to gain a better understanding of biological processes through both qualitative and quantitative analysis. As modern life science research becomes ever more quantitative, the need for mathematical modeling becomes ever more important. 当现代生命科学研究变得更加量化，建立数学模型的需求变得越来越重要。对复杂生物现象的深入理解最终是建立在了解发生于多时空间尺度的复杂生物学相互作用上，例如，分子尺度，细胞尺度，个体和群体尺度上。通过研究一些案例，我们将建立一些简化的数学模型以及其背后的基本数学框架。同时，我们将学习如何建立基本生物学过程的简单表征，以及如何定量和定性和定量地的分析这些模型，并将它们的结果以生物学的方式进行解释，以期提供实验学家进行检验的假说和预测。 How to construct simplified representations of biological processes and phenomena How to analyze mathematical models in a qualitative and quantitative manner...

Learn to use R programming to apply linear models to analyze data in life sciences. Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory online course in data analysis, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units....

Introduction to linear optimization, duality and the simplex algorithm. Introduction to linear optimization, duality and the simplex algorithm. The course is structured into 5 sections. Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem. Duality: you will learn how to derive a companion problem called the "dual"....

Take a deep dive intoPrime Numbers - one of the most mysterious and important subjects in mathematics! 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 are all prime numbers and they hold special significance. In this course, I will present several attractive topics on prime numbers. You will learn basic concepts of prime numbers from the beginning....

Introduction to unconstrained nonlinear optimization, Newton’s algorithms and descent methods. Introduction to unconstrained nonlinear optimization, Newton’s algorithms and descent methods. The course is structured into 6 sections: Formulation: you will learn from simple examples how to formulate, transform and characterize an optimization problem. Objective function: you will review the mathematical properties of the objective function that are important in optimization....

Introduction to network optimization and discrete optimization Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts....

Apply mathematics to solve real-life problems. Make a mathematical model that describes, solve and validates your problem. Improve your model. How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. In the verified track of this course you will additionally:...

Learn key mathematical tools necessary to anticipate the performance levels of queueing systems and understand the behavior of other systems that evolve randomly over time. Situations where resources are shared among users appear in a wide variety of domains, from lines at stores and toll booths to queues in telecommunication networks....

This course is an introduction to linear algebra. You will discover the basic objects of linear algebra – how to compute with them, how they fit together theoretically, and how they can be used to solve real problems. We will be emphasizing the vocabulary throughout, so that students become comfortable working with the different aspects....