Courses

Running the Numbers in Earth Science

Applications of mathematics in the Earth Sciences. Insights into many Earth materials and processes can be derived through the application of mathematics. Examples that are grade appropriate include:
  • Determination of the density of mineral and rock specimens
  • Determining stream discharge based on velocity and cross-sectional area measurements
  • Determination of the ability of a sediment to store and transmit water, determination
    of the weight percent of elements within environmentally important minerals and their relationship to atmospheric carbon dioxide concentration
  • Application of simple statistical measures to distinguish fossil species
  • Calculating the size of a dinosaur based on preserved track ways
  • Determining the rate of plate tectonic continental separation

Quantitative Mechanics

Students will be introduced to calculations in engineering physics with grade-appropriate problems of direct relevance and applicability. Fun and practical examples involving accessible vector algebra and trigonometry include:
  • Momentum conservation in jet and rocket propulsion
  • Projectile and ballistic trajectories – the trebuchet and the missile
  • Conservation of energy and roller-coaster physics
  • Bernoulli’s equation and aerodynamic lift
  • Fluid power and hydraulics
  • Automotive engine torque and vehicle acceleration

Computing and Quantitative Reasoning
Programming is inherently a problem solving activity, one which relies heavily on logical and quantitative reasoning. Students of all ages are naturally attracted to the graphical side of programming and the object-oriented nature of today’s languages make interesting problems very approachable to beginning programmers. Python is a high-level language which contains
a simple graphics component and encompasses all of the features of object-oriented programming (OOP). Many games, with rules that are quite simple, offer programming challenges that demonstrate the need for mathematical reasoning. Translating the logic
of a game into its physical manifestation in code, including elementary graphics, is an approachable but realistic problem for beginners to undertake. Students can come away
with a feeling of accomplishment at having produced a functioning game. Topics to
be included are:
  • Polya’s problem solving techniques
  • classes and methods in an OOP environment using libraries and pre-built functions
    to solve problems
  • simple graphical representations
  • walking through logic, both human and computer working as a team, i.e., the whole
    is greater than the sum of its parts

Environmental Mathematics

This course will address the importance of environmental awareness and action in our increasingly technological world. We will analyze environmental issues using mathematical techniques such as difference equations and regression. Appropriate topics include:
  • Environmental topics in the news
  • Population studies
  • Ground-level ozone
  • Environmental economics

Mathematical Problem Solving

Problem solving is central to inquiry and application. Well-chosen problems can be valuable
in developing or deepening students understanding of mathematical ideas. This course will
be activity based and will build new mathematical knowledge through problem solving. It will apply and adapt a variety of strategies to solve problems, encourage creative and non-routine solutions, and monitor and reflect on the variety of solution approaches available. Investigation of mathematics through problem solving can allow the students to experience the power of mathematics.

Geometric Reasoning

This course will consider several topics in two-and three-dimensional geometry. Participants
will use Geometer's Sketchpad to explore and make conjectures in several geometric situations. Hands on activities and models will be used to explore three dimensional polyhedral and spherical geometry. These activities are designed to expose students to diverse set of topics in geometry and to help them develop the reasoning skills needed to solve problems of a geometric nature.