Supplementary Notes on Restiaceae.

Supplementary Notes on Dedekind Cuts

Motivation: Our textbook discusses and even proves many properties of R, the field of real numbers; but it doesn’t define it. I felt that it would be rather awkward to discuss real numbers without knowing what they were and I decided to write some notes on the construction of R. The approach I am following is called ‘Dedekind cut’, discovered by a German mathematician, Richard Dedekind (1831-19...

Supplementary Notes

In a previous study in which we examined the genome-wide response of Arabidopsis to the xenobiotic compound trinitrotoluene (TNT) via cDNA microarrays, we found that Atwbc19 (At3g55130) was among upregulated genes. Given the role of ABC transporters in cellular detoxification we sought to further characterize this gene. Initial characterization of mutants revealed that root growth of Atwbc19 kn...

Supplementary Lecture Notes on Elliptic Curves

1. What is an elliptic curve? 2 2. Mordell-Weil Groups 5 2.1. The Group Law on a Smooth, Plane Cubic Curve 5 2.2. Reminders on Commutative Groups 8 2.3. Some Elementary Results on Mordell-Weil Groups 9 2.4. The Mordell-Weil Theorem 11 2.5. K-Analytic Lie Groups 13 3. Background on Algebraic Varieties 15 3.1. Affine Varieties 15 3.2. Projective Varieties 18 3.3. Homogeneous Nullstellensätze 20 3...

Supplementary Figures and Notes

Math 145: Supplementary Notes