## ACADEMIC CURRICULUM

Below are the descriptions of typical academic courses offered by the Young Scholars Program. Courses are subject to change year-to-year, and the below courses may or may not be available.

Each young scholar typically attends a total of three courses in the fields of

**mathematics**,**science**, and**computer programming**. The courses are designed specifically for this program, they are neither high school nor college courses.**We do not offer dual enrollment, high school or college credit.**While students' preferences are solicited and taken into account when making course assignments, the ultimate decision is up to the instructors. It is not first come, first served, and students may be placed in different courses than requested.

## MATHEMATICS COURSES

**Mathematical Models and Problem Solving**

This course is intended to help students develop their problem solving skills using mathematics as a tool. The course will involve two main activities: (a) classroom meetings where students will investigate and discuss strategies for solving problems in mathematics, and formulate mathematical models for problems arising in the natural sciences; (b) computer laboratory activities where students will investigate problems and models using Excel and possibly Geometers' Sketchpad. Students will be assessed on the basis of their participation and performance during class meetings, the quality of their homework assignments, and correctness and exposition on a group project. This course provides practical, interactive experiences in using mathematics for solving a diverse range of problems. Collaborative work will be encouraged throughout the course.

**Please bring a USB flash drive for this course.**

Examples of problems to be discussed:

- Model the evolution of an infection given a law for the spread of the infection.
- A power plant is to be located near three cities. Where should the plant be located such that the sum of the distances to the three cities is as small as possible?
- Given the birthrates, survival rates, and initial populations for each 10-year age group, determine the age distribution of the population in subsequent decades.
- Which numbers can be represented as the sum of two or more consecutive integers?
- Describe the polyhedra that can be constructed from faces that are pentagons and hexagons.

**Probability and Simulation**

Probability plays an indispensable role in our intellectual lives. Statements written in the language of probability can be found in almost all disciplines, from mathematics to the sciences, and engineering to the social sciences. Simulation is a computational tool based on probability. Just as repeated tosses of a coin can reveal the underlying probabilistic structure, simulation can be used to understand complicated probabilistic models.

In this course we will learn the basics of probability theory, and how it is used in computing, modeling, and algorithms. We will use simulation to develop an intuitive understanding of concepts from probability. We will also learn a simple, intuitive programming language called Julia, and use it to run our computer simulations.

## SCIENCE COURSES

**The Dynamic Organization of the Genome**

In this course, we will use eukaryotic cell models to explore examples of genome organization that broaden our fundamental understanding of gene regulation. We will work our way through the organization of the human genome, learn how genes are expressed, identify the potential of the genome in different cell types, identify epigenetic features of the genome, and map the structure of the genome. At every point in the course we will employ state of the art tools and techniques available at Florida State University. The course will consist of three approaches: genomics, microscopy, and proteomics. Critical thinking, interactive discussion, and hypothesis formulation will be emphasized. A strong desire for hands on experimentation is required.

**Physics of the 20th and 21st Centuries**

Our emphasis will be on physics of the 20th and 21st centuries, which is often called modern physics. Modern physics covers a wide range of topics that include atomic theory, statistical mechanics, wave theory, quantum physics, and relativity. These topics have relatively little overlap with high school physics course content, which levels the playing field for students of varying backgrounds, so long as they bring with them a strong interest in mathematics and problem solving. In this course, we will explore a variety of topics in modern physics, with an emphasis on critical thinking, problem solving, and interactive discussion. Experimentation and demonstration will be primarily computational in nature, relying heavily on interactive simulations, such as those available from PhET.

## PROGRAMMING COURSES

**Scientific Computing with C++**

This course will focus on instilling the core principles of computing into its students. Rather than approach the programming structure from a theoretical level, we will learn programming through an immersive and intuitive framework. Even from the very first day of class we will get our hands dirty, and after understanding the purpose behind our programs we will pull the curtains back and tackle the details involved in the examples. The C++ programming language will be used to explore the fundamentals behind computer science and in applying them to scientific programming. The primary objective in this course will be to learn the underlying principles involved in programming in an effort to understand how to learn on your own - learning new languages, new libraries, new algorithms, etc. We want you to see the big picture. This will be a very dynamic course. We will have certain concepts to cover each lesson, and examples to help illustrate them - but from there we will just play with code! After all, we learn the best when we're having fun.

**Computer Science with Python**

This course introduces advanced topics in Computer Science using the Python programming language. It is assumed that students have a basic understanding of computers and programming. The aim of the course is to introduce advanced topics using the Python programming language, such as data processing, graphical user interfaces, problem-solving with advanced algorithms, and writing programs to automatically access and analyze information from social networks (Facebook and/or Google and/or Twitter). The first three weeks will be devoted to learning how to program with Python, including practice assignments. The fourth week is devoted to data processing with file storage, followed by lectures and projects to learn and implement graphical user interfaces, advanced computer science algorithms, and online data analysis and principles of gaming. Each topic has a hands-on project the students can work on in class, in the laboratory, and off campus. Students will demonstrate their achievements after reaching each project milestone.

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