# Aim High 3 Teacher Book.104

Welcome to the online text resource for CH104: Chemistry and the Environment. This online text resource is also for the Willamette Promise College in High School Program. If you are a high school teacher and would like to join the Willamette Promise so that your high school students can start earning college credit in high school, please inquire at the Willamette Promise website.

## Aim High 3 Teacher Book.104

Feature Papers represent the most advanced research with significant potential for high impact in the field. FeaturePapers are submitted upon individual invitation or recommendation by the scientific editors and undergo peer reviewprior to publication.

This course is the first in a sequence of three calculus courses designed for students in the earth and mineral sciences and related fields. Topics include limits of functions, continuity; the definition of the derivative, various rules for computing derivatives (such as the product rule, quotient rule, and chain rule), implicit differentiation, higher-order derivatives, solving related rate problems, and applications of differentiation such as curve sketching, optimization problems, and Newton's method; the definition of the definite integral, computation of areas, the Fundamental Theorem of Calculus, integration by substitution, and various applications of integration such as computation of areas between two curves, volumes of solids, and work.

Fundamental concepts of arithmetic and geometry, including problem solving, number systems, and elementary number theory. For elementary and special education teacher certification candidates only. A student who has passed EDMTH 444 may not take MATH 200 for credit. MATH 200 Problem Solving in Mathematics (3) (GQ) This is a course in mathematics content for prospective elementary school teachers. Students are assumed to have successfully completed two years of high school algebra and one year of high school geometry. Students are expected to have reasonable arithmetic skills. The content and processes of mathematics are presented in this course to develop mathematical knowledge and skills and to develop positive attitudes toward mathematics. Problem solving is incorporated throughout the topics of number systems, number theory, probability, and geometry, giving future elementary school teachers tools to further explore mathematical content required to convey the usefulness, beauty and power of mathematics to their own students.

Mathematical ways of thinking, number sequences, numeracy, symmetry, regular polygons, plane curves, methods of counting, probability and data analysis. For elementary and special education teacher certification candidates only.

This course studies the foundations of elementary school mathematics with an emphasis on problem solving. MATH 201 Problem Solving in Mathematics II (3) (GQ) Problem Solving in Mathematics II studies the foundations of elementary school mathematics with an emphasis on problem solving. Mathematical ways of thinking are integrated throughout the study of probability, statistics, graphing, geometric shapes, and measurement. This course is designed for prospective teachers not only to gain the ability to explain the mathematics in elementary school courses, but also to help them comprehend the underlying mathematical concepts. Gaining a deeper understanding will enable them to assist their young students in the classroom since effective mathematical teaching requires understanding what students know, what they need to learn, and then helping them to learn it well.

Honors course in first- and second-order equations; special functions; Laplace transform solutions; higher order equations; Fourier series; partial differential equations. MATH 251H Honors Ordinary and Partial Differential Equations (4) This course serves as an introduction to ordinary and partial differential equations. Topics include various techniques for solving first and second order ordinary differential equations, an introduction to numerical methods, solving systems of two ordinary differential equations, nonlinear differential equations and stability, Laplace transforms, Fourier series, and partial differential equations.The typical delivery format for the course is four 50-minute lectures per week, with typical assessment tools including examinations, quizzes, homework, and writing __assignments.In__ contrast to the non-honors version of this course, the honors version is typically more theoretical and will often include more sophisticated problems. Moreover, certain topics are often discussed in more depth and are sometimes expanded to include applications which are not visited in the non-honors version of the course.

Development thorough understanding and technical mastery of foundations of modern geometry. MATH 313H Concepts of Geometry (3) The central aim of this course is to develop thorough understanding and technical mastery of foundations of modern geometry. Basic high school geometry is assumed; axioms are mentioned, but not used to deduce theorems. Approach in development of the Euclidean geometry of the plane and the 3-dimensional space is mostly synthetic with an emphasis on groups of transformations. Linear algebra is invoked to clarify and generalize the results in dimension 2 and 3 to any dimension. It culminates in the last part of the course where six 2-dimensional geometries and their symmetry groups are discussed. This course is a a part of a new "pre-MASS" program (PMASS)aimed at freshman/sophomore level students, which will operate in steady state in the spring semesters. This course is directly linked with a proposed course Math 313R, its 1-credit recitation component. It is highly recommended to all mathematics, physics and natural sciences majors who are graduate school bound, and is a great opportunity for all Schreyer Scholars. The following topics will be covered: Euclidean geometry of the plane (distance, isometries, scalar product of vectors, examples of isometries: rotations, reflections, translations, orientation, symmetries of planar figures, review of basic notions of group theory, cyclic and dihedral groups, classification of isometries of Euclidean plane, discrete groups of isometries and crystallographic restrictions. similarity transformations, selected results from classical Euclidean geometry}; Euclidean geometry of the 3-dimensional space and the sphere (distance, isometries, scalar product of vectors, planes and lines in the 3-dimensional space, normal vectors to planes, classification of pairs of lines, isometries with a fixed point: rotations and reflections, orientation, isometries of the sphere, classification of orientation-reversing isometries with a fixed point, finite groups of isometries of the 3-dimensional space, existence of a fixed point, examples: cyclic, dihedral, and groups of symmetries of Platonic solids, classification of isometries without fixed point: translations and screw-motions, intrinsic geometry of the sphere, elliptic plane: a first example of non-Euclidean geometry); Elements of linear algebra and its application to geometry in 2, 3, and n dimension (real and complex vector spaces. linear independence of vectors, basis and dimension, eigenvalues and eigenvectors, diagonalizable matrices, classification of matrices in dimension 2: elliptic, hyperbolic and parabolic matrices, orthogonal matrices and isometries of the n-dimensional space); Six 2-dimensional geometries (Projective geometry, affine geometry, inversions and conformal geometry, Euclidean geometry revisited, geometry of elliptic plane, hyperbolic geometry). The achievement of educational objectives will be assessed through weekly homework, class participation, and midterm and final exams.

Group work on challenging problems, discussions and project presentations. MATH 314 PMASS Problem Solving Seminar (1) A 1-credit Problem Solving Seminar will feature group work on challenging problems which require only elementary techniques for their solution. Each student of the PMASS program will be required to participate in two individual or group projects. Unlike those in MASS Program, the projects will not be necessarily closely related to the courses, although the course instructors will be encouraged to offer topics and supervise the work. Some projects will grow out of the work of the problem solving seminar, and the seminar will be a venue for the students to discuss their research projects. This course is a a part of a new "pre-MASS" program (PMASS)aimed at freshman/sophomore level students, which will operate in steady state in the spring semesters. This course is linked with other PMASS courses, and is highly recommended to all mathematics, physics and natural sciences majors who are graduate school bound, and is a great opportunity for all Schreyer Scholars. Each student of the PMASS program will be required to participate in two individual or group projects.The achievement of educational objectives will be assessed through evaluations of the project presentations.

Bi-weekly lecture series with multiple invite speakers. MATH 315 PMASS Colloquium (1) This bi-weekly lecture series will feature multiple invited speakers. Unlike MASS colloquia that focus on specific topics, those lectures will be broad in scope and not very technical.We envision that advanced high school students from State College Area High School will attend these lectures that will be properly advertised. This will help to attract talented high school students to undergraduate study of mathematics and related subjects, and will also enhance our existing collaboration with mathematics educators in the area. This course is a a part of a new "pre-MASS" program (PMASS)aimed at freshman/sophomore level students, which will operate in steady state in the spring semesters. This course is highly recommended to all mathematics, physics and natural sciences majors who are graduate school bound, and is a great opportunity for all Schreyer Scholars.

Development of a thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces. MATH 403H Honors Classical Analysis I (3)The central aim of this course is to develop thorough understanding and technical mastery of foundations of classical analysis in the framework of metric spaces rather than multidimensional Euclidean spaces. This level of abstraction is essential since it is in the background of functional analysis, a fundamental tool for modern mathematics and physics. Another motivation for studying analysis in this wider context is that many general results about functions of one or several real variables are more easily grasped at this more abstract level, and, besides, the same methods and techniques are applicable to a wider class of problems, e.g. to the study of function spaces. This approach also brings to high relief some of the fundamental connections between analysis on one hand and (higher) algebra and geometry on the other. This course is a sequel to Math 312H; it is highly recommended to all mathematics, physics and natural sciences majors who are graduate school bound, and is a great opportunity for all Schreyer Scholars. The following topics will be covered: Metric spaces (topology, convergence, Cauchy sequences and completeness); Maps between metric spaces (continuous maps and homeomorphisms, stronger continuity properties:uniform continuity, Hoelder and Lipschitz continuity, contraction mapping principle, points of discontinuity and the Baire Category Theorem); Compact metric spaces (continuity and compactness, connectedness, total boundedness, coverings and Lebesgue number, perfect metric spaces, characterization of Cantor sets, fractals); Function spaces (spaces of continuous maps, uniform continuity and equicontinuity,Arzela-Ascoli Theorem, uniform approximation by polynomials. Stone-Weierstrass Theorem).