## Overview

SVGS has programs and courses designed to meet the unique needs of gifted and highly motivated students. Students may attend in our Sciences (Science, Technology, Engineering and Mathematics) program. Students take a mathematics, science and technology class.

All first year science students must conduct an independent research or engineering project during the first semester. This project is formally within the purview of the Research and Engineering course. However, students may choose a project in any area of science, math or engineering that is interesting, provided a SVGS faculty mentor and a community mentor can be found if the project falls outside in-house areas of expertise. *Students are required to present their projects at the Student Research Symposium held each spring, at which attendance is mandatory for all science students. Students are also required to submit their projects to the Virginia Junior Academy of Science or an equivalent venue, and if accepted, required to attend the annual conference and/or competition. *

## Mathematics

**Governor’s School Pre-Calculus **– Students increase their understanding of functions and their characteristics including graphing techniques, using exponential, logarithmic and trigonometric functions to solve application problems, arithmetic and geometric sequences and series, mathematical induction, limits, first and second order derivatives, and integration. Students explore the use of mathematics in the natural sciences, thus fostering an application-oriented approach to mathematics that is enhanced through the use of technology. Students make extensive use of technology as an integral part of their learning. Students improve their facility with graphing calculators and the computer packages

*Maple and*

*Excel.*

**Governor’s School Calculus** – Students become proficient with limits, the derivative and differentiation techniques, the integral and integration techniques, basic applications of differentiation and integration, and infinite series, including Taylor Series. Students explore the fundamental relationship between the derivative, the integral, and the Riemann Sum. Students begin their study of multidimensional calculus including vectors and parametric equations. Students enhance their learning through computer-based activities utilizing* Maple *and* Excel. *Students must take this class for BRCC credit (Math 173-174, 5 credits each) at their own expense. Prerequisite: Any Pre-Calculus course.

**Governor’s School A. P. Calculus BC*** * – Students master limits, derivatives and anti-derivatives of polynomial, exponential and trigonometric functions and their inverses, as well as parametric, polar and vector functions for planar curves; techniques of differentiation and anti-differentiation; continuity of functions and the Intermediate Value Theorem and Mean Value Theorem; Fundamental Theorem of Calculus; physical applications of derivatives and anti-derivatives; series of constants and tests for convergence of series; Taylor’s series approximations of functions with radii of convergence and error bounding. Students actively participate in class discussions, which are supplemented by graphing calculator and computer activities. Students become proficient with *Maple *and* Excel.* This course prepares students to take the BC version of the Advanced Placement Calculus test, which is a required activity. Pre-requisite: SVGS Pre-Calculus (grade of A- or better) or a dual-enrollment pre-calculus class (grade of A- or better). Prerequisites may be waived by the Director.

**Advanced Calculus: Multivariable Calculus: **Concepts learned during the first year of calculus to advanced problems in multi-dimensional analysis. Students investigate topics including rectangular, spherical and cylindrical coordinates, three-dimensional vectors, partial differentiation, multiple integrals and matrices. Students’ understanding of multi-dimensional mathematics is enhanced with computer visualization techniques. This course is designed for students who have exceptional math skills. Pre-requisite: A.P. Calculus B.C. or SVGS Calculus (grade of B or better)

**Governor’s School Discrete Mathematics** – Discrete Mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. This course offers a nice counterpoint to the study of continuous mathematics that students pursue in calculus. Students will study logic, set theory, and matrices. Students will understand elementary number theory, the basic techniques of proof, and the basics of counting including combinatorics and probability. The ideas of discrete mathematics inform the study of computer science and this course will emphasize the connections between them. It is strongly recommended for students taking AP Computer Science. Students may take this course for dual-enrollment credit through JMU (Math/CS 227) at their own expense.

**Governor’s School A. P. Statistics** – Students become proficient with the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Four broad themes woven throughout the course are experimental design, measures of central tendency, anticipating patterns, mathematic modeling and statistical inference. Students enhance their understanding through the use of computer software packages such as *Excel* and *JMP*, which are used extensively to analyze, display and aide in the interpretation of data. This course prepares students to take the Advanced Placement Statistics test, which is a required activity. Pre-requisite: completion of Pre-Calculus (grade of C or better) and prior completion or concurrent enrollment in any Calculus class.

## Science

**Governor’s School College Physics** – Students conduct extensive laboratory investigations on topics including Newtonian mechanics, optics, electromagnetism, and materials science. Students’ investigations and assignments integrate the physical sciences with mathematics. Students enhance their learning through the use of technology to analyze and present data, and simulate experiments. Students may opt to take this class for dual enrollment credit with JMU (PHYS 140-140L/150-150L, 4 credits each semester)at their own expense .

** Governor’s School A. P. Chemistry – **Advance Placement Chemistry is designed to be equivalent to a first-year college chemistry course. Students will participate in lectures, demonstrations, activities & extensive laboratory experiments on topics such as atomic structure & quantum theory, chemical compounds, reactions & stoichiometry, states of matter & solutions, thermo-chemistry & kinetics, equilibrium, acids & bases, electro-chemistry, nuclear chemistry & organic chemistry. AP Chemistry also involves applying these concepts to “every-day” life with projects such as calorimetry, efficiency, crystal growth, catalysis and water treatment.

**Governor’s School Environmental Chemistry** – Students master basic principles of chemistry and statistical analysis in the context of the chemical and physical characteristics of water, soils, rocks, the atmosphere and natural fuels. Students conduct extensive laboratory analysis and field sampling utilizing EPA methods where feasible. Students investigate anthropogenic influences on natural materials cycles from the viewpoint of the classical chemist. Students enhance their learning through the use of instrumental analysis, which supplements traditional micro and wet chemistry methods. Students will demonstrate mastery of computerized data recording, calculation and analysis; graphical presentation; researching primary and popular literature; and formal report writing and scientific presentation. This class is required of any SVGS student who will not otherwise have completed high school chemistry prior to graduation. Students may opt to take the class for JMU credit (ISAT 112, 3 credits) at their own expense.

**Governor’s School A. P. Environmental Science*** * – Students explore geology, paleontology, atmospheric science, ecology, and technology in the context of environmental problems facing humans today. Students conduct extensive laboratory and field studies including water and air quality, soil processes, population dynamics, and community and ecosystem processes. Students enhance their learning through the use of computer simulations and models, and the use of technology to analyze and present data. Students are prepared to take the Advanced Placement Environmental Science test, which is a required activity. Pre-requisites: Biology, Chemistry, Physics and Pre-Calculus, completion of Earth Science is strongly recommended. Students may opt to take the class for JMU credit (ISAT 112, 3 credits) at their own expense.

**Governor’s School Molecular and Microbiology** – Students investigate fundamental life processes through the use and study of rapidly developing technologies such as genetic engineering, pharmaceutical developments, and treatment and prevention of infectious diseases. Students conduct extensive laboratory investigations on DNA extraction, gel electrophoresis, culture and identification of microbial organisms, and biochemistry. Students enhance their understanding of biological molecules through the use of mechanical and computer molecular modeling. Students become proficient in the use of technology to analyze and present data. Students may opt to take this class for dual enrollment credit with JMU at their own expense (ISAT 113, 3 credits). Pre-requisites: Biology, Chemistry, Physics (all with grades of B or better) and Pre-Calculus.

**Governor’s School Modern Physics** – Students explore the theoretical study of Special Relativity and Quantum Mechanics with an emphasis on computer models of the processes involved. Topics covered include Special Relativity, the Schrödinger equation, tunneling phenomena, General Relativity, Elementary Particle Physics, and the Hydrogen Atom. Students enhance their learning through extensive laboratory investigations and simulations. Students become proficient in the use of technology to analyze and present data. Pre-requisites: GS Physics, and GS Pre-Calculus or GS Calculus (grades of A- or better). Co-requisite: Calculus or above.*(Offered pending enrollment.)*

## Technology Courses

**Governor’s School Scientific Research*** * – Students discover and put into practice research methods and engineering design. Students apply principles of the natural sciences and applied statistics in solving research and engineering problems. Students complete an individual research project, write a scientific paper, and submit their results for presentation at various venues, including the SVGS Research Symposium (participation is required) and Virginia Junior Academy of Science (paper submission and participation, if accepted, is required). They make use of on-line libraries and review scholarly scientific resources.

**Governor’s School Engineering I ***–* Introduction to Engineering familiarizes students with the engineering design process in a project-based learning environment. Toolkit skills such as dimensional analysis, computer-aided design, and statistical analysis will be introduced and incorporated in projects throughout the year. A project-based approach to the major branches of engineering (Electrical, Civil, Mechanical, and Chemical) will give students the opportunity to apply engineering design principles to a variety of problems while developing personal skills in teamwork and communication that are vital in the engineering profession.

**Governor’s School Advanced Technology**** ** – The primary focus in Advanced Technology is the exploration of computer technology as a tool for communicating powerful ideas in mathematics and science. Students learn to animate in two-dimensions and build interactive presentations. Students will learn to create web sites and will develop an understanding of good design. Students will also explore digital photography and digital video production. The students will use all their skills to build pod-casts and other means of using MP3 players such as iPods. The course is project-based and students will develop projects in conjunction with their mathematics and science courses. Students will also be asked to discuss ethical issues related to modern technology and to learn vocabulary associated with computers.

**Governor’s School A. P. Computer Science (A) ** – Students design, implement and interpret computer-based solutions to problems in several application areas using *Java.* Students become knowledgeable about programming concepts, algorithm designs, and documentation of the computer solution and proficient at writing and debugging code. The course material emphasizes those concepts outlined by the College Board and prepares students to take the Advanced Placement Computer Science test. Students may opt to take this class for dual enrollment credit with Blue Ridge Community College at their own expense (ITP 120, 3 credits). Pre-requisites: completion of Pre-Calculus, Research and Engineering, and Physics (grades of A- or better) OR permission of the Director and Instructor.

** Governor’s School Computer Network Software Operations/Networking Security – **Students are provides instruction in the basics of computer networking, operating systems, system administration and network security. Course content includes a overview of networking, operating systems and other software applications, learning to perform common administrative functions in scripting environments. Students will examine PHP and PERL in the context of an Apache webserver, and use GNU BASH and Microsoft Powershell scripting from the command line to complete every day administrative functions. Course content also includes risk management, network security policy, security training, security keys, confidentiality, integrity, acess, accountability, and audit ability.

*Participation in various industry sponsored contests*

*such as Cyber Challenge and other contests*

*are expected.*

*Course offering is dependent on student interest, sufficient enrollment and staffing.*

**Governor’s School Engineering II** – Students develop the “thought-work” behind applying concepts of multi-disciplinary engineering methods. Students are immediately immersed in advanced tenements of: static and dynamic equilibrium of particles, tools, and complex elements (like the human body); use of Computer Aided Design in basic engineering modeling; test and evaluation concepts; evaluation of structural and mechanical relationships; evaluation and application of problem design criteria, design for failure concepts, precision and safety-factors mark some but are not inclusive of all the principals touched-on during the course. Engineering Methodology combines mathematics and the physical sciences to resolve problems and reverse engineer solutions. Students complete a dozen team Design Projects and solutions are presented via CAD, schematics, and detailed technical write-ups. Individuals improve math, physics and material science skills by combining them to resolve problems. As part of this class, students may opt to enroll in the first semester of the University of Virginia’s Introduction to Engineering (ENGR1520, 3 credits) at their own expense.

**Governor’s School Geospatial Information Systems **– Students will develop the skills and knowledge necessary to make use of geographic technologies such as geospatial information systems (GIS), global positioning systems (GPS), and remote sensing. The class will focus on applying GIS technology to different fields, such as environmental science, city planning, ecology and many others. Students will work with a variety of data sets, collect data, and develop their own GIS research project. Students in this class must enroll for dual enrollment credit with James Madison University at their expense (GEOG 161 , 3 credits).

**Governor’s School Electric Vehicle Technology ** – Students study, create and implement designs of electrical circuits and mechanical devices based on the needs of an electric vehicle. Students create web pages to explain their cars, develop trouble-shooting methods, make presentations, and investigate environmental issues related to transportation. The hands-on approach to this course enables students to develop personally, academically, and professionally. Students compete in organized electric vehicle meets, where they learn racing strategies and safety as well as new and innovative ways to improve the school’s vehicle design.