Math and Statistics Resources
Mathematics, statistics, and actuarial science at Purdue is difficult; as a Purdue math graduate, I have first-hand experience with the program. I've put together this collection of resources for your use based on references that I found most useful during my time there.
I find every resource here useful, however, I don't expect that you'll use every single one. Pick and choose among what works for you and your study routine.
The most important thing to remember about college math is that most of your learning takes place OUTSIDE of the classroom!
Resources WITHIN Purdue: These resources come directly through Purdue; therefore, they should be reasonably consistent with what you are learning in class.
Chenflix: Professor Chen has recordings of lectures for several math classes.
Math Department Past Exams Archive: I used this all the time in my undergraduate career in calculus I, II, and III. This is NOT the same as Boiler Exams!
I would start with the most recent exams and work backwards.
Math Library: Great references here. You can also check out the books you use in class if you can't purchase or get a textbook right away.
Math Help Room: Good for homework help and group studying.
ASC: The academic success center. They also have supplemental instruction for classes outside of math, too.
Resources OUTSIDE of Purdue: These are good resources but be cautious: since they come from math/stat courses outside of Purdue, they may not be as coordinated with what you are learning depending on the textbooks used, the overall degree of difficulty of the course, etc.
Paul's Online Math Notes: Great supplemental notes and problems (many with answers) for college algebra, calculus I, II, III and differential equations.
College Algebra: https://tutorial.math.lamar.edu/Classes/Alg/Alg.aspx
Calculus I: https://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
Calculus II: https://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx
Calculus III: https://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx
Differential Equations: https://tutorial.math.lamar.edu/Classes/DE/DE.aspx
Clark Bray: A Duke teaching professor with good video notes for multivariable calculus and linear algebra.
MIT OCW: MIT's Opencourseware was flipping the classroom before it was popular. You can search by course name for non-math courses, as they have quite a bit in their library.
Linear Algebra I (like MA 351): https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011/
Linear Algebra II (like MA 35301): https://ocw.mit.edu/courses/18-700-linear-algebra-fall-2013/
Differential Equations (like MA 366): https://ocw.mit.edu/courses/18-03-differential-equations-spring-2010/
Complex Analysis (like MA 425): https://ocw.mit.edu/courses/18-04-complex-variables-with-applications-spring-2018/
Abstract Algebra (like MA 453): https://ocw.mit.edu/courses/18-703-modern-algebra-spring-2013/pages/syllabus/
Penn State Statistics: Useful for stats. Purdue equivalent in parentheses () at end of hyperlink.
STAT 414 Introduction to Probability Theory: https://online.stat.psu.edu/stat414/ (STAT 416)
STAT 415 Introduction to Mathematical Statistics: https://online.stat.psu.edu/stat415/ (STAT 417)
STAT 480/481/482: Topics in SAS: https://online.stat.psu.edu/stat480/ https://online.stat.psu.edu/stat481/ https://online.stat.psu.edu/stat482/ (STAT 506)
STAT 484/485: Topics in R: https://online.stat.psu.edu/stat484-485/ (no Purdue equivalent but useful if you want to learn R)
STAT 500 Applied Statistics: https://online.stat.psu.edu/stat500/ (STAT 350/511)
STAT 501 Regression Methods: https://online.stat.psu.edu/stat501/ (STAT 512)
STAT 502 Analysis of Variance and Design of Experiments: https://online.stat.psu.edu/stat502/ (STAT 512 and STAT 514)
STAT 505 Applied Multivariate Statistical Analysis: https://online.stat.psu.edu/stat505/ (STAT 524)
STAT 506 Sampling Theory and Methods: https://online.stat.psu.edu/stat506/ (STAT 522)
STAT 510 Applied Time Series Analysis: https://online.stat.psu.edu/stat510/ (STAT 420/520)
Cosma Shalizi: CMU stats professor. His notes on modern regression (like STAT 512) and statistical computing (like STAT 506) are great with the following caveats:
Modern regression notes use a different version of the STAT 512 book at Purdue. It is also more math-heavy than STAT 512.
Statistical computing uses R, whereas STAT 506 uses SAS.
Reference Textbooks: If you can spare the cash, I've found these books to be among the best reference texts one can have on hand. Some may be available online, others at Purdue's math library. The links are to Amazon.
Calculus III/Vector Calculus (MA 261, 362):
Multivariable Calculus by Clark Bray (comes with a YouTube course on this channel)
Great intuition for calc 3. Few places have multivariable calculus as difficult (or harder) as Purdue, but Duke is definitely one of them!
Intro to Proofs/Real Analysis (MA 301, 341)
Proofs: A Long-Form Mathematics Textbook by Jay Cummings
Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings
I don't own either of these, however, what I've read from them is extremely clear.
Real Analysis/Advanced Calculus (MA 301, 341, 440, 442, etc.):
Calculus by Michael Spivak (answer book here)
The best reference book in the business! My all-time favorite calculus/analysis book; best answers to "why" questions.
Linear Algebra (MA 351):
Introduction to Linear Algebra by Gilbert Strang
Gilbert Strang is the champion of linear algebra. His MIT 18.06 course and webpage are legendary.
Differential Equations (MA 266/366/303):
Ordinary Differential Equations by Morris Tennenbaum and Harry Pollard
There is a FREE Internet Archive version of this book here!
The notation is a little outdated but answers to all problems are provided. WolframAlpha can help fill in intermediate steps.
(The book mentions but does not explicitly cover partial differential equations, so it's not a perfect fit for MA 303; but it's close!)
Probability (STAT 311, MA/STAT 416, STAT 516, STAT 519):
Introduction to Probability by Joe Blitzstein and Jessica Hwang
There is a FREE version of the second edition of this book here!
Great explanations! Includes links to Harvard video course.
An Introduction to Probability Theory and its Applications Volume 1 by William Feller (aka "Feller Volume 1")
A classic! Definitely read if you have the time.
Introduction to Probability Theory by Hoel, Port, and Stone
Another good probability book.
Complex Analysis (MA 425):
Introduction to Complex Analysis by Michael Taylor
A First Course in Complex Analysis by Matthias Beck, Gerald Marchesi, Dennis Pixton, and Lucas Sabalka
These are recommended in the MIT OpenCourseWare course for complex analysis.
How to Study Math
My advice is below. (I'm assuming a similar pattern works for physics but as I was not a physics major, I cannot say for sure.)
1. Engage with the textbook: read it before AND after lecture. Reading before lectures helps you preview new topics and will help the fast paced college-style lectures make more sense. Reading after lecture helps solidify what you've learned. Read the textbook slowly and carefully, being sure you can follow all steps in a problem. Work the example problems yourself while you read, covering the solution with an index card.
2. Attend ALL lectures AND recitations.
3. Do your homework. All of it. On time.
4. Study continuously throughout the term, NOT just the night before the exam. Start preparing for midterms at least two weeks in advance.
5. When studying, work out a wide variety of problems on a blank sheet of paper WITHOUT referring to books/notes/examples, etc. AND WITHOUT using a calculator! Do this for as many problems as you can get your hands on.
The rest of this section is borrowed from Clark Bray of Duke University.
The TL;DR for below is: (1) Go to class, (2) Read the book before AND after class, (3) Do the homework, (4) Study throughout the term, not just the night before an exam.
Lectures
Be on time, and be sure to sit in a location where you can comfortably see the board and easily hear the lecturer.
Do not have your email, Facebook, YouTube, or other distractions open during the lecture. Note, these are distracting also to the students behind you!
Have either an electronic or paper copy of the lecture notes, and annotate with your own notes throughout the lecture. Use colored pens to distinguish your notes.
If you are confused by some portion of the lecture, and if lecture recordings are being made, make a note of the time at the corresponding location on the lecture notes. This will allow you to easily locate the relevant portion of the video when you return at a later time to study this portion of the notes.
Review the lecture recordings for every class meeting. You might spend some time with other resources first, to try to resolve some prerequisite issues that might have been holding you back during class. When you are ready, click through to the parts of the lecture that you found most confusing.
Reading
Before each lecture, skim over the appropriate pages of the lecture notes, and the corresponding sections of the book.
After the lecture, re-read the above thoroughly. Remember, you are responsible for all of the material in the book and in the notes (unless explicitly stated otherwise), but due to time constraints not all will be covered in class.
Homework
After each lecture and the subsequent reading, you should try to complete as many of the homework exercises from that day as you can, and make as much progress as you can on the others, to avoid leaving too many exercises to be done just before the due date.
Note the Help Room hours and course office hours, and plan your schedule to allow you opportunities to go to ask questions specifically about exercises that you could not complete on your own.
Go to the Help Room or course office hours to get help on the questions from the previous day, complete all of those exercises, and submit that assignment.
Try also to go to the Help Room or office hours with general questions on the material that might have come up in your mind as a result of the homework exercises.
Plan your schedule also to allow you to come to instructor office hours with questions, especially general questions for which you might get the best help from the instructors.
Daily studying
Identify important topics covered that day, relevant definitions, theorems, techniques, and applications.
Identify topics you are having trouble with. Identify if those topics make use of earlier topics you are continuing to have trouble with.
Spend focused time reading the presentation of that material in the lecture notes and in the book.
Consider reviewing relevant portions of the lecture recordings, if such recordings are being made. (Work back-and-forth between the written materials and the lecture recordings -- watching the recordings can help you understand things in the written materials, and likewise understanding the written material can help you understand further in the recordings.)
Maintain a list of questions to ask in instructor office hours, or the help room, that get specifically to what you are having trouble with. Ask these questions in office hours or the Help Room. Cross off questions when resolved, or consider rephrasing if your concerns are not thoroughly satisfied.
Big-picture studying
Identify how current topics from class relate to, and/or make use of, earlier topics from the course.
Think about why topics have been presented in this order.
Try to anticipate possible generalizations or applications of recent topics.
Discuss the above with a study group of other students.
Organization
Maintain a documented daily schedule that allows you to fit in the above items, along with the rest of your obligations.
Adjust your daily schedule as you gain experience on how best to allocate time to these items.
Consider how your schedule might need to change near an exam date.
Consider how you might make most effective use of the flexibility of time during the weekend.
Physics Resources
This is borrowed from Janice's page.
Purdue Career Resources for PHYS students
1. Career Development Resources
College of Science - Career Development make an appointment with Danielle Sheese!
Society of Physics Students -Career Resources
Center for Career Opportunities: CCO
Document writing resources : SPS resources, My CCO resources
2. Undergraduate Research
- How do I obtain a research experience?
Students obtain research experience in a variety of ways (both on–campus and around the country and globe) – through their professors and department, the National Science Foundation , Discovery Park , for–profit companies, non–profit organizations, and personal contacts.
Physics Resarch Opportunities: Physics Research Overview, Undergraduate Research Information
Office of Undergraduate Research (OUR): https://www.purdue.edu/undergrad-research/
College of Science -Internship/Research
3. Summer Internships
Looking for a Job/Internship:
Get Started
MyCCO portal
LinkedIn
Ripplematch
Internships.com
Career Research Portal
Purdue Pathmaker: https://www.itap.purdue.edu/pathmaker/
Indianaintern.net & Earn Indiana: https://indianaintern.net/
SPS Jobs: https://jobs.spsnational.org/
USA Jobs: https://www.usajobs.gov/Search/ExploreOpportunities/?Series=1310
Dice: http://www.dice.com/
Indeed.com: https://www.indeed.com/
LinkedIn: https://www.linkedin.com/job/home/
Society of Physics Students - Summer Research/Internships
SURF at Purdue: https://engineering.purdue.edu/Engr/Research/SURF
REU sites for ASTRONOMICAL SCIENCES: http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=5045
REU sites for PHYSICS: http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=69
REU sites for DEPARTMENT OF DEFENSE: http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=10023
Los Alamos National Laboratory – https://www.lanl.gov/careers/career-options/student-internships/undergraduate/index.php
Argonne National Laboratory –Undergrad Internship Opportunities: https://www.anl.gov/education/undergraduate-internship-opportunities
Department of Energy (SULI): https://science.osti.gov/wdts/suli
Pathway to Science research opportunities
IAESTE global opportunities
U. S. Dept. of Energy http://science.energy.gov/wdts/
ORISE's online application system (Oak Ridge Institute for Science and Education)
4. International Students
Los Alamos National Laboratory – https://www.lanl.gov/careers/career-options/student-internships/undergraduate/index.php
Argonne National Laboratory –Undergrad Internship Opportunities: https://www.anl.gov/education/undergraduate-internship-opportunities