Course Outline: Phys 114, Spring 2017

Introduction to Data Reduction with Applications (3-0-3)

Co-requisites: Math 111

Instructor: Dr. John Federici, Office: 474T, 596-8482; email:

Office Hours: Tuesdays and Thursdays 2:30-3:30pm or by appointment

Synopsis: An introduction to both the theory and application of error analysis and data reduction methodology. Topics include the binomial distribution and its simplification to Gaussian and Poisson probability distribution functions, estimation of moments, and propagation of uncertainty. Forward modeling, including least-squares fitting of linear and polynomial functions, is discussed. The course enables students to apply the concepts of data reduction and error analysis using data analysis software applied to real data sets found in the physical sciences.


  Course Materials: Free online textbooks

As a supplemental textbook (purchase not required), try to find a copy online of Data Reduction and Error Analysis for the Physical Science (3rd Edition), by Philip R. Bevington and D. Keith Robinson.

  MATLAB (available for download from NJIT web page) or similar analysis and plotting software. NOTE: The course has standardized on MATLAB, but if you wish to use another software package (eg. Mathcad, Mathematica, etc.) PLEASE DISCUSS with your instructor... Quizzes and exams may contain MATLAB questions.

  Note: The homework assignments will be distributed via the world wide web. The course webpage can be accessed through the following web address:


ATTENDANCE: It is expected that students will attend all lectures, recitations, etc. If you anticipate an absence, please let your instructor know immediately. If you miss any in-class exercises, it is YOUR responsibility to make arrangements with the instructor to make up the assignment outside of normal class hours. Absence from class DOES NOT alter the deadlines for turning in assignments or taking exams.


HELP:   Visit or email your instructor if you are having trouble with the course; do not simply hope for a miracle and fall further behind.


GRADING:  Your final letter grade in Phys 114 will be based on a composite score for term’s work that includes the mid-term, final exam, and homework.

  • Homework - Homework is given every week and is considered an important part of the class. The homework usually consists of reading the text, short answer questions, and numerous mathematical calculations. Homework assignments are given in the syllabus below and are due weekly. Late homework will NOT be accepted.

  • ExamsThe purpose of the exams is to test the individual student's progress in the class. Exams are closed book/notes. Exams will be announced ahead of time. In the event of a student missing an exam, the physics department policy for 'make up' exams will be followed. 

  • In-class quizzes and class participation - There will be short, in-class quizzes at random times roughly every 2-3 weeks. In addition, attendance at lecture is expected and will be rewarded.

Final Letter Grades : Here are the approximate weights to be used for calculating the composite score:

  18%  for first exam

  18%  for 2nd Exam

  19% for Final Exam

  25% for Homework

  10% for In-Class quizzes and class Participation

  10% for Final In-class Project


The cutoff percentages for various letter grades will be in the range of  85% for A, 80 % for B+, 75% for B, 70% for C+, 60% for C, 55% for D, and F below 55 %.


HONOR CODE STATEMENT:  NJIT has a zero-tolerance policy for cheating of any kind and for student behavior that disrupts learning by others.  Violations will be reported to the Dean of Students.  The penalties range from a minimum of failure in the course plus disciplinary probation up to expulsion from NJIT.  Avoid situations where your own behavior could be misinterpreted as dishonorable.  Students are required to agree to the NJIT Honor Code on each exam, assignment, quiz, etc. for the course.


Turn off all cellular phones, wireless devices, computers, and messaging devices of all kinds during exams and lecture portion of class. For inclass assignments, the instructor will let you know when to turn on your computers. Please do not eat, drink, or create noise in class that interferes with the work of other students or instructors.   Creating noise or otherwise interfering with the work of the class will not be tolerated.


Assignments: You are responsible for all weekly reading and homework assignments listed in this outline. The reading should be completed BEFORE class each week. Homework assignments MUST be turned in ON TIME. Homework assignments are due just about EVERY WEEK. Check syllabus weekly to see what is due. ALL ASSIGNMENTS not turned in by the assigned date will be scored as a zero. Each student must turn in individual Homework assignments. No group submissions will be accepted.


Course Policy on Submitting Matlab Code:

If for any homework problem or class project that requires you to submit Matlab code please use one of the following options:

(a)  Make sure that the location of any input files is included in the file path in which Matlab searches (use PATHTOOL command in Matlab).

(b) The submitted code via must be ‘stand-alone’. This means that if your instructor copies and pastes your code into Matlab it should run WITHOUT any errors. To ensure that this is true, when you download any data files from the course web page which will be imported into Matlab, DO NOT change the name(s) of any input files.

(c)  If you define any Matlab functions which are required for your code to run, you must include the functions as a Matlab file as an attachment to your homework.

(d) Prior to submitting your HW assignment or other Matlab assignments, you should VERIFY that your Matlab code will run WITHOUT any execution errors.


EMail/ Alternative Methods of Delivery Policy: The instructor is not responsible for assignments turned in outside of class time (in my mailbox, under my door) or not delivered by email. If assignments are delivered by email, it must be date stamped BEFORE the due date/ time. I will log them in when I receive them. THE INSTRUCTOR IS NOT RESPONSIBLE FOR LOST EMAILS, COMPUTER CRASHES, ETC.


Groups and Working Together: With regards to homework assignments, you are encouraged to work together if that method helps you learn the material. However, each student must submit an individual homework assignment with their own analysis, graphs, and discussion. DO NOT CUT AND PASTE your homework from other students’ work. However, remember that you must understand the homework assignment well enough that you can do it BY YOURSELF on the exams.


LEARNING OUTCOMES: For this course, you can expect to be assessed on the following learning outcomes:

  1. Be able to address the pros and cons of various methods of measurement

  2. Be conversant with the data reduction and error analysis concepts mentioned above,

  3. Be able to analyze 1D and 2D data sets to find computational estimates of PDFs, moments, and to address the appropriateness of various forward models,

  4. Be familiar with various measurement techniques so as to best experimentally determine PDFs, moments, and the appropriateness of various forward models,

  5. Be able to devise an experiment capable of making a measurement to a pre-determined level of precision,

  6. Be able to create figures that are journal-quality,

  7. Be extremely familiar with the Matlab software package so as to utilize it in subsequent classes and research endeavors.


Topic/ Text Assignment (with Lecture Note Links)

HW Problems



Review of MatLAB: capabilities and programming environment
Forms of data (vectors, arrays, images as numbers)
APPLICATION: Write a basic MatLAB program Lecture01

Making plots Lecture02
Using HELP

Defining Functions – Homework Submissions of MATLAB CODE

APPLICATION: Write a basic MatLAB program to plot generated data

Download MatLab from NJIT Website


Info on finding Summer Research

More MatLAB
Basic matrix/array operations for reading in data and for graphical output

Do's and Don'ts of Journal Quality Figures Lecture03 

Lines or dots- Additional notes on 'good plots' using Matlab

Image Data Cartoon and histograms Lecture04
APPLICATION: Write a basic MatLAB program to read in real data and make a plot Lecture3-SampleData.xls Lecture3-SampleData.txt

HW #2





Uncertainties in Measurement: - Sections 1, 4-8. - Sections 1.1-1.2, 2.5, 2.7 - Sections 0, 1

Accuracy, Precision, Systematic/ Statistical Errors,

Parent/Sample Distributions

Mean, Median, Mode, Variance, Standard Deviation

Percent error, SNR—reduction of noise through repeated measurements
APPLICATION: Random Noise and Systematic Noise in THz Time-Domain Transmission measurements. Lecture06

HW #3

avg1, avg3, avg6, avg10, avg30, avg60, avg100, avg300


Discrete Probability Distribution Functions: - Sections 3 - Sections 4.1,4.2,4.3, 4.6, also read KEY TERMS and CHAPTER REVIEW for Chapter 4.

Binomial Lecture07 and Poisson PDFs Lecture08

HW #4


Continuous Probability Distribution Functions: - Sections 5.1, 6.1, 6.2 - Sections 4,5.

Gaussian PDF, and other noise: White Noise and 1/f noise. Lecture09 - Section 9
Statistical Uncertainty and Propagation of Errors
Lecture10, Lecture 11 Lecture11_example matlab code

HW #5


Exam 1: In class   


Error Analysis

Averages of averages, Central Limit Theorem, 'Bad' data points - Sections 7.1-7.3 Section 11.

APPLICATION: Affects of averaging in an experiment

HW #7


Confidence Intervals, Student's t-Test, Chi-Squared test, Goodness of Fit - Sections 8.1-8.2 - Sections 11.1-11.2

Lecture 13

HW #8

HW8 Problem 3 Data


Fitting of Data to Linear Functions - Chapter 12


Linear least squares fitting. Lecture 14, Lecture 14a

Chi-Square and R-square fitting. Uncertainty in fitting parameters.

Data set For Class Exercise Lecture 14


HW #9


EXAM 2: In-class  


Linear Fits for Polynomial, Linearization of Fitting Equation Lecture 15


Nonlinear fitting - Custom and 'arbitrary' fitting, Generalized least-squares fitting.

'culling' of data in matlab. Lecture 16 CLASS EXERCISE DATA
APPLICATION: Fitting of Interferometer data to measure motion of moving object with sub-wavelength resolution.







Fourier Transforms, Nonlinear Fitting of THz Spectrum, Prepare for Final Project



In-Class Project Final project hints



Final Project Instructions

Journal Paper Template



Final Project, REVIEW for FINAL



Spring Break March 12-19

Tuesday May 2nd follows a FRIDAY schedule

READING DAYs – May 3-4