UPDATE PATTERNS IN (ENVIRONMENTAL) MATH SPRING 2026 SITARAMAN
PATTERNS IN (ENVIRONMENTAL) MATH 12 Section 1 SPRING 2026 UPDATE PAGE
SITARAMAN
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Welcome! On this page you will see updates on what we did in class,
what is coming up, solutions to tests, etc., Keep checking!
Course Page with syllabus, grading policy and general information
Office hours MWF 3 to 4 pm Office 219 ASB-B
Other times email me at ssitaraman AT howard.edu (NOT bison.howard).
Zoom link for virtual meetings that might be necessary will be posted on Canvas.
Welcome.
Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,
Here is what we did last time I taught this class:
UPDATE PAGE FROM SPRING 2025
Not everything will be the same but you can get an idea.
QUIZZES AND ORAL PRESENTATIONS ARE 40% OF GRADE. IF YOU PAY ATTENTION, EASY TO GET THEM RIGHT.
Weekly quizzes are worth 140 for the semester, but there maybe some extra credit at the end. There will also be oral presentations in my office, worth 60 points.
MANY OF THE CLASS NOTES BELOW WILL CONTAIN QUIZ PROBLEM SUGGESTIONS.
CHECK AT LEAST ONCE A WEEK!!
Started 1/12/2026
PLEASE READ ALL INSTRUCTIONS ABOVE AND KEEP UP WITH CLASS.
4/1/26 Wednesday
Today we talked about standard deviation and variance. They help us understand how the values are dispersed
What we did in class including example calculation is all
in these notes on standard deviation. Please try the Practice problems in the above notes. You could have similar problems in Quiz on wednesday.
Notes from Spring 19 (thanks to Dr. McGowan) on Statistics.
3/30/26 Monday
Today we talked about measures of central tendency such as mean, median, mode, and percentile.
What we did in class including example calculation is all
in these notes on central tendency measures such as average (mean) and median. Please try the Practice problems in the above notes. You could have similar problems in Quiz on wednesday.
Notes from Spring 19 (thanks to Dr. McGowan) on Statistics.
3/27/2026 Friday
Please read Quiz 6 solutions.
QUIZ 6 PROBLEMS.
QUIZ 6 SOLUTIONS.
Quiz 6 Graph.
Quiz 6 friday this week: adding numbers in geometric sequence, statistics collecting and presenting data.
PLEASE STUDY THE NOTES FROM 3/20, 3/23, 3/25 AND WORK ON PRACTICE PROBLEMS AT THE END OF EACH NOTES.
We watched this
video about Simpson
s paradox which is a strange occurrence in statistics where trends like average look different when calculated over larger sets of data.
We will talk about averages next week. For the quiz, it is enough to study in the notes from today, monday (3/23) and friday (3/20).
Today we talked about presenting data and making charts.
What we did in class including example calculation is all
in these notes on importance of statistics and about collecting data. Please try the Practice problems in the above notes. You could have similar problems in Quiz on friday.
Notes from Spring 19 (thanks to Dr. McGowan) on Statistics.
3/23/26 Monday
Today we talked about collecting and organizing data and the importance of statistics.
What we did in class including example calculation is all
in these notes on importance of statistics and about collecting data. Please try the Practice problems in the above notes. You could have similar problems in Quiz on friday.
Notes from Spring 19 (thanks to Dr. McGowan) on Statistics.
3/20/26 Friday
Today we talked about adding numbers in a geometric sequence and mortgage monthly payment formula.
Notes from 2019 on Geometric sequences and Exponential Functions.
What we did in class including example calculation is all
in these notes on adding the numbers in a geometric sequence.
Please try the Practice problems in the above notes. You could have similar problems in Quiz next friday.
3/18/2026 Wednesday
Please read Test II solutions.
TEST II PROBLEMS.
TEST II SOLUTIONS.
TEST 2 on WED MAR 18.
PLEASE COMPLETE ORAL PRESENTATIONS PART 2 BY MAR 6.
Will cover quadratic equations, parabola graph, geometric sequence, compound interest, continuous growth and decay, and exponential functions.
PLEASE BRING A REGULAR CALCULATOR. CELLPHONES CANNOT BE USED TO CALCULATE.
Please study: CLASS NOTES, Quiz solutions,
PROBLEM 1, 2, 3 of
Test 2 version A and Problems 2, 3 of
Test 2 version B .
Problems 3, 8, 9, 10 of
Test 1 version A and
Test 1 version B.
Qns 2, 4, and 5 from midterm from Spring 22
3/4/2026 Wednesday
Please read quiz solutions. Extra credit 10 points for this quiz.
QUIZ 5 PROBLEMS.
QUIZ 5 SOLUTIONS.
QUIZ 5 will cover finding n-th term of geometric sequence and compound interest formula, difference between exponential and polynomial and power functions,
doubling time for geoemtric growth, and growth when it happens many times a year and also continuously. Please go over the notes from each class starting monday 2/23 and do the practice problems given inside the notes, at the end.
2/27/26 Friday
Today we talked about continuous growth and decay, and also doubling time.
We also watched this video on carbon dating of bones
We also listened to this talk on climate change and carbon dating.
Notes from 2019 on Geometric sequences and Exponential Functions.
What we did in class including example calculation is all
in these notes on continuous growth and decay.
Please try the Practice problems in the above notes. You could have similar problems in Quiz wed (except for the half-life and decay problems).
2/27/26 Friday
Today we talked about growth when it happens many times a year and also continuously, and also doubling time.
Notes from 2019 on Geometric sequences and Exponential Functions.
What we did in class is all here, including example calculation,
in these notes on Exponential functions and continuous growth.
Please try the Practice problems in the above notes. You could have similar problems in Quiz next wed.
2/25/26 Wednesday
Today we talked about difference between exponential and polynomial and power functions, and more on using compound interest formula.
We also watched this video on exponential growth
Notes from 2019 on Geometric sequences and Exponential Functions.
What we did in class is all here, including example calculation,
in these notes on Exponential functions and compound interest formula.
Please try the Practice problems in the above notes. You could have similar problems in Quiz next wed.
Monday, 2/23/2026.
Today we talked more about finding n-th term of geometric sequence and compound interest formula.
Notes from 2019 on Geometric sequences and Exponential Functions.
What we did in class is all here, including example calculation
in these notes on Applications of quadratic functions and geometric sequences
Please try the Practice problems in the above notes. You could have similar problems in Quiz next wed.
2/20/2026 friday
Please read quiz solutions.
QUIZ 4 PROBLEMS.
QUIZ 4 SOLUTIONS.
Wednesday, 2/18/2026.
QUIZ 4 ON FEB 20. STUDY QUADRATIC EQUATION, PARABOLA, AND
GEOMETRIC SEQUENCE.
Sample problems are: Identifying geometric sequence and finding common ratio,
finding focus of a parabolic object, graphing parabola given by a quadratic equation.
Today we talked more about applications of quadratic functions and how to graph parabola and find its focus. We also started geometric sequences.
Notes from 2019 on Quadratic Functions and Parabola.
What we did in class is all here, including example calculation :
Applications of quadratic functions and geometric sequences
Please try the Practice problems in the above notes.
2/16/26 Monday.
The heating system in ASB-B has been fixed. On wednesday we will meet in usual room.
2/13/2026 friday
Please read Test I solutions.
TEST I PROBLEMS.
TEST I SOLUTIONS.
TEST I ON FRI, FEB 13. Review mon 2/9.
Will cover basics of climate change, averages and probability, scientific notation, basics of climate change, big numbers,
number systems, linear functions and arithmetic sequences.
PLEASE BRING A REGULAR CALCULATOR. CELLPHONES CANNOT BE USED TO CALCULATE.
Please study: CLASS NOTES, Quiz solutions,
PROBLEMS 1 to 7 of
Test 1 version A solutions.
Test 1 version B solutions.
Qns 1,2, 3 from midterm from Spring 22,
Wednesday, 2/11/2026. 4:30pm
Today we talked about applications of quadratic functions and how to graph parabola and find its focus.
Notes from 2019 on Quadratic Functions and Parabola.
What we did in class is all here, including example calculation :
How to identify and graph quadratic functions
Please try the Practice problems in the above notes.
2/11/26 Wednesday, 10:20 am.
Because our heating system in ASB-B is not working well, class will be on zoom today. Zoom link is in the announcements.
TEST 1 WILL BE IN CLASS ON FRIDAY. I will be in office until 4pm today if you need anything.
What we do in class today will not be on this test.
2/9/2026 Monday
Today we did a review for Test I. If you were not in class please talk to someone who was.
2/6/2026 friday
Please read quiz solutions.
QUIZ 3 PROBLEMS.
QUIZ 3 SOLUTIONS.
Wednesday, 2/4/2026.
Today we talked about applications of linear functions and also about arithmetic sequences.
Notes from 2019 on Linear Functions and Arithmetic Sequences.
It's all here, including example calculation :
How to identify and write arithmetic sequences
How to add the numbers in an arithmetic sequences
Please try the Practice problems in the above notes.
Tuesday, 2/3/2026.
Yesterday we talked about what graphs of linear functions.
It's all here, including example calculation : Notes from Yesterday.
Please try the Practice problems in the above notes.
1/30/2026 friday
Please read quiz solutions.
QUIZ 2 PROBLEMS.
QUIZ 2 SOLUTIONS.
Thursday, 1/29/2026.
Quiz 2 tomorrow on number systems, number bases such as base 2, base 10 and base 20, graphs, correlation v causation.
Wednesday, 1/28/2026.
Today we talked about what graphs mean and how to interpret them.
It's all here, including example calculation and poll questions : Notes from Today.
Please try the Practice problems in the above notes.
1/23/2026 friday
Please read quiz solutions.
QUIZ 1 PROBLEMS.
QUIZ 1 SOLUTIONS.
Wednesday, 1/21/2026.
Today we talked about number systems from different civilizations, and how to convert from decimal to binary or vigesimal (base 20) systems.
It's all here, including example calculation : Notes from Today.
Please watch the video Pi and the Fibonacci Sequence .
Friday, 1/16/2026.
Today we talked about numbers, scientific notation, and units such as kilowatt, megawatt, etc.,
It's all here, including example calculation : Notes from Today.
This article on how solar and wind are meeting new demand
has a graph showing the various quantities in TWh (TeraWatthours).
Check out this article: Are there more stars than there are grains of sand on Earth?
We then watched the video Is Success Due to Hard Work or Luck ?.
There maybe a question in the first quiz (next friday 1/23) about scientific notation and units and big numbers.
Thursday, 1/15/2026.
Yesterday we talked about climate change and averages.
We did an example Calculation of Average Winnings.
This includes a bit of probability. We will discuss probability and statistics in more detail, later.
We then watched the video "climate change 101" (see below).
Please watch the other two videos also, before coming to class friday. Both are below.
There maybe a question in the first quiz (next friday 1/23) about average winnings, climate change and its causes or the difference between weather and climate.
Monday, 1/12/2026.
Today we got to know ourselves and talked about course.
We then watched the video "weather vs climate" (see below).
Please watch the other two videos also, before coming to class wednesday. Both are below.
There maybe a question in the first quiz (next friday) about climate change and its causes or the difference between weather and climate.
Friday, 1/9/2026.
Solutions from Spring 2025 final:
Final exam problems.
Final exam solutions.
Instructions for preparing for first class on Monday 1/12/2026.
IMPORTANT:Whether doing the Quizzes or Tests, you are expected, by the Honor code of the university, to do the work by yourself.
Any violation will result in forfeiture of quiz or test grade or even an F in class.
We will have quizzes almost each week, and questions and suggestions will be given during class, and they will count for 28% of grade. Only correct answers get credit.
Please watch the following videos. We will see examples of how math is used in studying climate change during class.
WHAT IS CLIMATE CHANGE? VIDEO: climate change 101
WEATHER VS CLIMATE
THE ECONOMIC INJUSTICE OF PLASTIC