Chapter 1 Review of necessary mathematical skills Spring 2016

About us Lab coach: Hao (Howard) Jin Email: jinhao@indiana.edu Oncourse and Course Website: http://haojin.weebly.com/ Office hours : Fridays 3:30 – 5:30 pm @ Wylie Hall 117 Grader: Seung Yeon (Sunny) Yoo Email: sy21@indiana.edu

Housekeeping In order that you receive all credit that you have rightfully earned, it is absolutely imperative that you unambiguously identify yourself on any assignment, document or message exchange that you submit, turn in or email. To do this you must include 1) your name, 2) your student ID number and 3) your lab section number (4199 or 4200) on any paper you turn in, any Oncourse submission and any email message sent to undergraduate interns, graders, lab coaches or professor over the entire semester. There are Excel tutorials to be found at this URL: http://www.gcearnfree.org/excel2013.

Nature of lab class Lab is the other half of the course and is, thus, integrated with lecture class. Lab is required course component, and constitutes one quarter of students’ final grade. Lab is centered on applications of concepts currently under discussion. Work through the lab manual chapter before coming to lab using a computer. You are not expected to be an expert when you come to lab, but you need to be familiar with the concepts and commands. Complete the pre-lab quiz and hand it in before the class begins. Feel free to raise questions during class.

Structure of the lab Hand in the pre-lab quiz. Briefly review the relevant information from lecture. Summarize the key points of lab manual chapter. Go through solutions to demonstration problems similar to the end of the chapter in the lab manual You will be given a set of problems to solve and hand in at the end of each lab. You can consult your neighbors, any references and also ask me for help.

TODAY’s Objectives Learn summation notation Refresh skills in working with fractions Be able to interpret the slope and the intercept coefficients of a linear equation Be able to distinguish different types of data

Summation notation 𝑖=1 100 𝑋 𝑖 = 𝑋 1 + 𝑋 2 +…+ 𝑋 100 𝑖=1 100 𝑋 𝑖 = 𝑋 1 + 𝑋 2 +…+ 𝑋 100 𝑖=1 𝑛 𝑐𝑋 𝑖 =𝑐 𝑖=1 𝑛 𝑋 𝑖 𝑖=1 𝑛 (𝑋 𝑖 + 𝑌 𝑖 )= 𝑖=1 𝑛 𝑋 𝑖 + 𝑖=1 𝑛 𝑌 𝑖 ( 𝑖=1 𝑛 𝑋 𝑖 )( 𝑖=1 𝑛 𝑌 𝑖 )≠ 𝑖=1 𝑛 𝑋 𝑖 𝑌 𝑖

Fractions 𝑎 𝑏 + 𝑐 𝑑 = 𝑎𝑑+𝑏𝑐 𝑏𝑑 ≠ 𝑎+𝑐 𝑏+𝑑 𝑎 𝑏 × 𝑐 𝑑 = 𝑎𝑐 𝑏𝑑 𝑎 𝑏 ÷ 𝑐 𝑑 = 𝑎𝑑 𝑏𝑐

linear relationship 𝑌=𝑚𝑋+𝑏 m is slope and b is intercept. The slope, m, is interpreted as the change in Y for one unit change in X. The intercept, b, is interpreted as the value of Y when X=0. Note: Do not forget the units of X and Y

Types of data Categories of Data Types of Data Qualitative or Categorical Nominal: named categories (e.g. eye color: blue/black/brown) Ordinal: categories with an implied order (e.g. restaurant rankings: very good/good/fine/bad/very bad) Quantitative, Numerical or Interval Discrete (e.g. number of kids) Continuous (e.g. length of a song)

Hierarchy of data types Continuous add unique values Discrete add magnitude Ordinal add logical ordering Nominal add more categories Binary Additional information