10 Oct 99 Thoughts and stuff: Math Projects for High School Students: 1) Ways to estimate pi -- convergence? error? - circumscribe, inscribe regular polygons - monte carlo methods - series representations 2) Random # Generation 3) Constructions - which angles can be constructed by compass & straightedge? origami? 4) Combinatorics & generating functions 5) Tests for logic problems - unique solutions? 6) Construct a slide rule - how does it work? 7) Construct calculators - how do they work? binary, floating pt errors 8) financial instruments - linear programming 9) Estimating Markov models - language/music 10) Dynamic Programming - finance, DNA sequence matching 11) asymptotics - solns of quadratic, cubic eqns 12) Numerical integration Notes from Math Problems in the Molecular Science: -------------------------------------------------- Bioinformatics -> function from sequence <- functional genomics rapid development - punctuated equilibria mutation matrix - amino acids to other ones point accepted mutations figure out form/structure from evolutionary trees sequence matching =cannot= be simply stochastic -- remember natural selection!!!!! sequence of edits? rocking back & forth walking back & forth different levels of codes in DNA & RNA -- junk? its not junk - used for structure (necessary to be able to copy, edit, etc.) 1) transcription code 2) DNA shape - certain doublets - give a certain 2ndary structure 3) chromatin - where to put the nucleosomes (wind around the histones) RNA 1) triplet 2) gene splicing 3) RNA processing 4) translation framing code 5) translation parsing code 6) folding 7) mRNA editing only 4% of original b.p. are found in code for end protein -- lots of introns cut out, other edits go on linguistic complexity defn -- for thought of ability to code on multi-levels U word usage A actual vocab size M maximal possible vocab size i word size n sequence length C = \product_{i=1}^{n-1} U_i U_i = A/M C = 1 --> maximally complex logarithmic word size --> least usage ARE WE NOT DRAWN ONWARDS WE JEWS DRAWN ONWARD TO NEW ERA molecular recognition - "shape recognition" lock-key large folded proteins - entropy, parallelism 3D chips? DNA analogs analog maze solver - microfluids 2D world -> 3D world micro-origami -> assemble minimize pushing & shoving easy folds, minimum deformation -> make small antennae (fractal antennae) emergence complexity question: development, cortical folding? End of Science Dynamic allocation cell death & removal pointers Apoptosis don't =care= about R!!! (what?) non-stochastic mitochondrial DNA phylogeny make =fake= phylogeny Math sucks in all of them => other things: mplot - see if that's already defined xvector/matrix -> xmin xmax yvector -> ymin ymax fit button zoom button type - regular pts, etc.

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