Wednesday, January 30, 2013

Week0: CK-12 Resources

CK-12 is an incredible STEM resource. Log on to it and peruse the subjects you want to learn.  The site is designed to offer self-paced learning, achievement tracking, grade based content.  Perhaps most significant is the ability of the student and educator to create eFlexBooks  in .mobi, .epub, and PDF formats. The mathematical and statistical lessons are of very high quality. And this resource is free.  Check out these two flexbooks:
This type of resource allows an opportunity for myself as an instructor to discuss how technology increases learning. I highly recommend the use of a portable reader such as a Nook or Kindle or the use of reader software on your smart phone or laptop. Simply put, mathematics is sometimes best learned in small doses at places convenient for the student. To prevent visual fatigue from interfering with comprehension, I prefer a reader that handles the display of Greek Letters with optimum clarity in all types of light.

For these articles, the student may find a resource on the use of Greek Letters in Mathematics helpful. Please see my (upcoming) post on the use of greek letters in mathematics and their representation in statistical software.

Questions for the Students
For this course on data science we are very interested in
  1. statistical concepts
  2. mathematical concepts that are critical to statistical programming
Mathematical structures important to statistical programming include:
  1. the concept of a function
  2. the properties of arrays, vectors, matrices and other data structures
Read pages 5 - 62 in  CK-12-MathAnalysis . Pay particular attention to the generic discussion of functions as a mathematical concept.  Read pages 42 - 73 in Basic-Probability-and-Statistics---A-Short-Course.
  • How do we understand visual data through graphs?
  • How is our understanding of visual data linked to mathematical concepts that represent data?
Both these works will prepare  a student for better understanding statistical software packages like R, Octave, Python, Scilab.

For the ambitious
Read Probability and Statistics - Advanced(Second Edition) .  If you find your eyes glazing over when reviewing formulas, try this strategy:
  1. Complete a first read of this work that skims over each chapter.
  2. Try to identify the general purpose of the discussion on data analysis in statistics.
  3. Take a break and think some about what you have read.
  4. Read the work carefully from one end to the other over a period of sittings. Each time you read something new, take some time to think about possible uses of the mathematical concept.

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