Linear Overview:



Topic Headings**  Description 

Learn some of the terminology surrounding number systems to the base N, with emphasis on those used in computing. Discuss positional notation systems with Roman Numerals for contrast. Research the history of computing devices, from the abacus until the present time. Preview exponential notation. 

Develop cardinal sense by looking at symbols paired with unique binary identifiers as per ASCII and Unicode mappings, contrast with ordinal sense. Consider alphanumeric addressing schemes such as URIs for webbased resources. Disucuss the omnipresence of relational data bases in contemporary society. Review hexadecimal numbers. Look at greaterthan, lessthan and equals operators in the context of the number line as an organizing heuristic. 

Review basic operations and corresponding algorithms. Include exponentiation. Introduce computer programs as algorithms. Explore logic gates in hardware, and more complicated circuits such as the halfadder. 

Contrast groups and fields using integer modulo multiplication and addition. Review raising to a power. Apply Fermat's Little Theorem to the task of determining primality. Review basic group theory. Discuss the RSA algorithm in the context of the field of cryptology, its history and applications. Preview extended Euclidean Algorithm in this context. 

Build a fraction object to support basic operations, including division of fractions, with GCD and LCD as integral functions. 

Develop an understanding regarding the relatioship between decimals and reals. Preview trigonometry by introducing the Pythagorean Theorem and the distance formula. Introduce log and exp operations. Preview functions vs. inverse functions. 

Introduce the generic concept of a relation as a set of ordered (domain, range) pairs, functions as a subset of relation. Review permutations when discussing composition of functions. Preview polynomials. Discuss inverse functions, along with various common types of functions and their graphs on the XY plane 

Develop the relationship between number sequences and geometric figures, both on the plane and in space. Use the jitterbug transformation to bridge the cuboctahedron and icosahedron. Given these shapes may be developed from packed spheres, discuss common sphere packing arrangements and their applications in architecture, biology, chemistry and crystallography. 

Introduce sigma and pi notation, factorials. Review recursion. Look at continued fractions, especially for roots, e and pi. Review SternBrocot tree. 

Discuss the difference between permutations and arrangements and derive the relevant formulae. Generate Pascal's Triangle and locate sequences. Revisit polynomial objects in a ring algebra and dervive the Binomial Theorem. Relate Pascal's Triangle to the Gaussian distribution and discuss probability and statistical concepts. Review factorial, sigma and pi notations. 

Discuss the complex plane, convergence, fractals. Review recursion. Preview Galois Theory regarding roots of polynomials, building on group theory concepts. 

Discuss the parts and types of triangles and strategies for computing their measures, given partial information. Define the trig functions and their inverse functions. Preview polyhedra when discussing polygons. Look at complex numbers in conjunction with the unit circle. 

Introduce Fuller's concentric hierarchy while reviewing sphere packing concepts and the octet truss. Use Euler's Law and Descartes' deficit to determine various measures. Discuss various coordinate systems and the concept of symmetry groups. Begin building polyhedra as objects. 

Explore simulations of complex systems, including those exhibiting nonlinear and/or chaotic features. Deepen understanding of modeling techniques and the relationship between models and actual phenomena. 

Build vector objects after looking at the historical challenges addressed by vector mathematics, in physics especially. Review polyhedra in light of these new tools. Consider polyhedra as objects with inherited methods for scaling, rotation and translation. 

Introduce the calculus using the motion picture analogy. Use Newton's Method to find nth roots of a real number, developing the geometric relationship between the derivative and slope at a point. Introduce integration as the inverse of differentiation. Introduce hyperbolic trig functions when discussing the catenary (a common curve). Review roots of polynomials in the complex plane in the context of LaGuerre's Method. Preview some vector calculus concepts. 
** underlined topic headings link to essays Oregon Curriculum Network 