Mathematics 110
Mondays
and Wednesdays, 1:302:50
Hegeman
308: Daniel Newsome Presiding
Email: bardmath@mifami.org 
Office Hours: By
appointment. Please feel free to email
me for an appointment. Seriously. Parent
Webpage: http://www.mifami.org 
Textbook: Precalculus
by Collingwood, Prince, and Conroy.
Open source text, dated
June 19, 2019.
Link to PDF .
Updated: 5/20/20 2:10 PM
Date 
Assignment 
Zoom
ClassesExtrasOptionsAddenda 
Last Class Wed 5/20 Class 16b Last Class 
PreCalculus to Calculus Our final
class attempts to connect the dots between precalc and calc. Final
Class Video: PreCalctoCalc
[ca. 45'] It ran a bit
longer than I anticipated, so let's meet up on Zoom at 2:30. That's
Zoom at 2:30. Again, no
new homework. Just make that last
assignment as good as you can. Here's
that link... again: Ch18HWPDF 
All backhomework
that you want me to see should be submitted to me by Monday, May, 25th. Final Tunes: 
Mon 5/18 Class 16a 
Tangents Today's
class looks at the tangent. What it
tells us. How to interpret its numerical
value. How it fits into the unit
circle. How to graph it. Class Video: Tangenti.mp4
[ca. 30'] Watch the video and join the Zoom class at 2:15. That's 2:15. No new homework. Just work on
the stuff due next Monday. Here's the
link... again: Ch18HWPDF 
This may assist
you with the final homework assignment. Nice little
interactive diagram for tangent here: link One more class on
Wednesday. 
Wed 5/13 Class 15b 
Addendum: The Travelling Sine Wave Today we
look at the travelling sine wave. This class
refers to some ideas from Chapter 19 of our text. It mostly focuses on the "phase
shift" and how that can be utilized to move a wave. I
recommend reading over Chapter 19 (expecially the summary on p262). This will help you with the homework
assigned on Monday. Class
Video: The
Travelling Sine Wave [video ca. 47'] Watch this
video and join the Zoom class at 2:45.
That's 2:45. There is
no new homework, just the homework assigned on Monday. Here's the
link... again: Ch18HWPDF The second
part of this homework assignment is sort of the final project for this
class. We are not having a final exam,
just this final homework project. Do
your best to make this both mathematically substantial and a beautiful,
creative presentation. Go nuts. Use your special talents, be they drawing,
music, video production, speaking, writing, dance... whatever. Have fun with it. 
All backhomework
that you want me to see should be submitted to me by Monday, May, 25th. Next week: We will have a Zoom class like normal on
Monday and our final class on Wednesday will be sort of an overview class. Again... Grades: Please email me
with the lowest letter grade you would like before I give you a pass or
fail. E.g. Let's say
your GPA is 3.0. You would not want
anything lower than a B, because this would lower you GPA. Relaxation Blues: Bit Louder: 
Mon 5/11 Class 15a 
Chapter 18: Trigonometric Functions Watch these 2 videos and join the Zoom class at 2:30. That's 2:30. Class Videos for Monday, 5/11/2020: Pt1: ch18.pt1WhiteboardSawSine
video Pt2: ch18.pt2Blackboardsinewavevideo The
Pythagorean Theorem in Trig. Notation cos^{2}(q) + sin^{2}(q) = 1^{2}. Remember,
1 is the radius of the unit circle. Homework: Ch18HWPDF The first part
of this assignment is due next Monday.
The second part is due the next Monday after class is over. 
Grades: Please email me
with the lowest letter grade you would like before I give you a pass or
fail. E.g. Let's say
your GPA is 3.0. You would not want
anything lower than a B, because this would lower you GPA. Zoom Class 5/11/2020 Nothing of importance in this Zoom Class so I'm not posting it. 
Wed 5/6 Class 14b 
Chapter 17b: Addendum Geometry and Trig. Watch this video and join the Zoom class at 2:10. Class Video for 5/6/2020: PolyPerimeter.mp4 Homework
PDF: Polygon and Perimeters: Due next Wednesday. 
Posted 5/20/20: Solution to Polygon to Perimeters Assignment: PolyPerimetersvideo Not much content in this one. Homework tutoring session this Sunday at 4:00 on Zoom. I'll send a Zoom invitation on Saturday. 
Mon 5/4 Class 14a 
Read Chapter 17: The Circular Functions. This is where we finally get sine, cosine, and tangent. SOHCAHTOA Sine is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. Class Video: Ch17video Watch it and join Zoom at 2:20 or so... The Homework assignment is described here: HWCh17.pdf

Full Solution to 17.5a.jpg. The Example 17.1.1 on p221 is a bit unclear. [I was bothered because there was no
mention of the cue ball.] The example
is simply describing the trajectory of a ball bouncing off the rail/cushion
of a pool table. Here's a 5 second
animation showing the situation: BilliardBall.mp4 Latitude
from GoogleMapsvideo Sad Tune from Keats [The] spirit is too weak; mortality Weighs heavily on me like unwilling sleep, And each imagined pinnacle and steep Of godlike hardship tells me I must die, Like a sick eagle looking towards the sky. Rockin' Andalucia 
Wed. 4/29 Class 13a 
Chapter 16: Measuring Circular Motion Watch these video and join the Zoom meeting at 2:00. Class Video 1: Ch16BicycleGearing
[17:30] Class Video 2: Ch16Conversions.mp4
[10:13] Due for Monday, April 4th. Assignment: Read over Ch.16. Do the following: 16.1, 16.2,
16.3a, 16.3c, 16.6. Turn in complete writeup for 16.6 (all
parts) [include useful drawings, prose,
and explanation of method. Please
circle or highlight all results.] Also Turn in: Figure out the centripital
acceleration and gforces acting on Michael in problem 16.6, using these
equations: [link to image] How long will Michael survive on
this ride? Should it really be called a
"merry"goround? Come up with a new name for this
ride. 
Terrible Quality 5280ft = 1 mile 12 inches = 1 foot 1 inch = 2.54 cm I will have a
homework tutoring session on Sunday at 6:00 pm. I'll send out a
Zoom invitation for this later this week. New Old Tunes 
Mon. 4/27 
Advising Day. No Class. 

Wed. 4/22 Class 12b 
Chapter 15: Measuring an
Angle Class Video 1: Circumference
to Radian [ca. 14'] Class Video 2: DegreeMinSecRadianConversions
[ca. 16'] Homework: Read Ch15 and do
the following problems at the end of the chapter: 1, 2, 5, 7, 8 Turn in: Problem 15.5. Add to this problem a nice
diagram and a short discussion of the various ways this calculation is not
completely accurate, but close enough. Turn in: Problem 15.7f Turn in: Problem 15.8. Just show the calculations with enough
prose to make it readable. Nothing
fancy. Here's a video with the
setup for 15.8: 15.8Setupvideo The full solution  15.8full solution
video 
2020.4.22ZoomClass
[ca. 14'] Entertainment 
Mon. 4/20 Class 12a 
MesoCh14&15:
Base Systems ...et plus Here are
the premade video presenations for Class. Video Class Part 1 [ca. 12'] Paper Folding to Proxima
Centauri This assignment will count as a quiz and is due next Monday. Here is the quiz. Due next Monday (4/27). Folding
to Proxima CentauriPDFform See Video Class Part 1 for context. Video Class Part 2: "Base
Systems Vid" [ca. 19'] The first section is poorly made. Sorry about that. The PDF will better explain some of this
stuff. Additional Video to help with making the
Spreadsheet: ExcelBaseConverterTutorial Assignment
on Bases due Wednesday: The actual
turnin assignment is described on p7. Here's how you get the answer: Base13to10video 
2020.4.20ZoomClass
[37'] Bluesy
Tunes riffin' on Here's
the talk I gave last Friday to the Physics Pholks: "As
Above. So Below" or Science. Yesterday's
Solutions Today's
Problems 
Wed. 4/15 Class 11b 
Ch14:
Rational Functions Chapter 14:
Class Video [39:08] Look over Ch14. Ch14 Homework Assignment:
some solutions provided. Added 4.26.2020 Helpful Hints: 14.5 calculation
details: There are many ways to do these calculations. Here is one way. 
Ian's 14.1c  Nice and
tidy and to the point, with good commentary. 2020.4.15Ch14ZoomPart(edited)
[6:25] Psychedelic Rap DGBeware.mp3with Manson
and Jane's Calmer 
Mon. 4/13 class11a 
Ch13: 3
Construction Tools Look
over Chapter 13. Do this: Chapter 13
Assignment 
Optional: Lipsitch4.13.20Who
Is Immune to the Coronavirus%3FNYT.pdf Wheat and Chessboard: Rice Volume
video and writeup. Nick's
Excellent Transforms Super presentation of various transformations. Take a
Break with: Distorted RealityCI1/4Tone Hippy Flam. L&MND Dance RT: Tekit... 
Wed. 4/8 class10b 
Ch12: Log Functions Read over Chapter 12. Do all of 12.1 and 12.8 in the exercises. Then read and do all the exercises on this
PDF: Newton's
Cooling and Radio Carbon Dating Turn in: Send me a screen shot of
#10, the spreadsheet you make ...
...and write up 14b (the papyrus scroll). Write it up completely, with a little
research on Egyptian texts thrown in to give it context. Fictional setups, illustrations, and
graphs encouraged. 
Watching
Water... Cool: Video 1 Watching Water
Cool: Video 2 Use either one for assignment. Making
the Cooling Spreadsheet: video Update: Solution: Here is a GoogleSheet with
a working spreadsheet: link Here is an Excel version of the same: link Nuclear
Bombs and Dating Carbon NYTimes Wheat
and Chessboard: Rice Volume
video and writeup. Break
Time: Buddy H on H: LROJB.mp3 Optional: 
Mon. 4/6 class10a 
Read
Chapter 11: Exponential Modeling Then
read this: Compount
Interest HomeWork, and do the exercises in it. No need to turn in. Answers included. Do this
and turn in: Wheat
and Chessboard Problem Write up a nice explanation and send it along
to bardmath@mifami.org. 
Finally,
this one is watchable. The New
Remote Math Study Room is now OneonOne tutoring. Contact Olive at: blc@bard.edu for an appointment. A very
nice writeup
of the Wheat and Chessboard Problem by BeiTong. Optional:

Wed. 4/1 class9b 
Chapter 10 Read Ch10: Exponential Functions
AND Read this: Ch10restrictions
on expfunction.pdf
AND Watch this: Tuning with
Daniel: Video
AND Do the following problems: 10.2, 10.3, and 10.4. Turn in: 10.2e and 10.4b. [Turn in here: bardmath@mifami.org.] Please title your files properly. 
Optional Digressions: The Jazz Kittens on
Instagram Cool Jazz on Ice The Visage of a Virus:
Visualizing CoVid19 
Finish
up all the SIR assignments and turn them in here: bardmath@mifami.org. Alert: All homework must be labled
as seen here: LastNameAssignmentName.ext E.g. NewsomeCh10.pdf or NewsomeSIR.jpeg I screwed up
a video setting in Zoom and the video quality is terrible in parts. (Experimenting
with Sound Tracks) 
Now,
for something completely different...Black Holes 

SIR Modeling Materials and
Assignment 
RadioLabPatient Zero
Excellent episode. Interesting use of sound and music. QuammenMalariaModeling
Describes the history of mathematical modeling (SIR model) NYTimesInteresting Graphics
Virus on the Move This is another approach to modeling the
infection. 





Update 3/21/2020: I've moved this entire assignment to its own page for
organizational reasons. Here it is: SIR Modeling Materials and
Assignment This is the
full assignment for 3/30 and 4/1. 
Intro Video
on Modeling an Epidemic: WelcomeToRemotePreCalculus.m4v I made a short video doing 9.7a. Use your Bard Google account
for access. Over Break Additional Materials: RadioLabPatient
Zero Excellent episode. Interesting use of sound and music. QuammenMalariaModeling
Describes the history of mathematical modeling (SIR model) 

This class
is moving online. Everything will be
orchestrated from this website. Ch9:
Inverse Functions. Read over this
chapter. It's actually pretty good. Do these
problems: 9.1a, 9.1b, 9.2a, 9.2b, 9.3, 9.5, 9.7a, and 9.9. Turn in this problem: 9.7a: Put both lines on the same graph and then
draw in y = x. Notice the symmetry
across y = x. Turn
this in electronically to: bardmath@mifami.org. 
Essentially you are
doing this: The range of one is the
domain of the other, and vice versa. Graphically inverting y = x^{2} [not by
best work] Homework
Email: Must
Read: The New Normal Page 



I've moved
the first half of the assignments (the ones we have done already)
to a new
page in order to clean up this page, which was getting cluttered.
The older
(previrus) assignments are now here:
Textbook: Precalculus
by Collingwood, Prince, and Conroy.
Open source text, dated
June 19, 2019.
Link to PDF
Useful Graphing
Calculator: GeoGebra.
[Geogebra Classic 5 can be
downloaded and used offline. Scroll down
to download to a computer.]
You can also use Geogebra
6 online or as an app on a phone.
Another popular one is desmos. There is no offline version that I am aware
of.
Math Study Room 
Now OneonOne tutoring.
Contact Olive: blc@bard.edu
Sunday 
Monday 
Tuesday 
Wednesday 
Julia Sheffler 
Jiangli Liu 
Yuexin Ma, (Echo) 
Riti Bahl 
Riti Bahl temporarily 
Felicia Flores 
Yiyang Zhou 
t.b.a. 
Please use this online resource.
Our tutors
need the work and would be happy to help out.
Description of Class
"A course for students
who intend to take calculus and need to acquire the necessary skills in algebra
and trigonometry. The concept of function is stressed, with particular
attention given to linear, quadratic,
general polynomial, trigonometric, exponential, and logarithmic functions. Graphing in the Cartesian plane and
developing the trigonometric functions
as circular functions are included."
Course Catelogue
Expectations
Treat this class like a job.
Show up on time, do the expected work on time, don't ask for extensions,
and don't make excuses.
If you cannot make it to class, email me [dnewsome@bard.edu] and let me
know in advance. I don't need to know
why.
Obviously, emergencies and special situations may occur and these will
be accomidated when appropriate.
Grading
This class is mostly about participating and taking the homework
seriously.
The quizzes and exams are just coersive ways to make you take the
homework seriously.
Grade breakdown:
Homework:
50%
Participation: 25%
Quizzes and Exams: 25%
The homework is
the most important part of this class.
There will be homework assigned for each class. Only certain problems from the assigned
homework will be turned in, so these problems need to be done like a short
essay. The problem needs to be restated
or clearly paraphrased. Diagrams (if
useful) need to be drawn and drawn well.
Prose commentary needs to be written to guide the reader (me) through
your thought process. Interesting
mathematical work needs to be shown. If
there is an equal sign, it had better be equal.
Answers need to be highlighted or circled or somehow made obvious. Also, useful additional sources should be
cited. [If you use a Khan Academy video,
provide a link. If you use another
textbook, cite it. If you use the Math
Study Room, say so.] If you cannot solve
the problem, you should figure out an estimate... an approximation... an
educated guess... draw some diagrams and write that up as your homework. Simply stating, "I couldn't figure it
out," is not good enough. Provide a
range within which you expect to find the answer, even if you can't figure out
how to set up the mathematics. Most
homework that you turn in will require multiple drafts. I want to see the second (or third) draft,
not the first. Messy first drafts with
only the calculations will not be given much credit.
And remember, in most of the homework problems most of the numbers will have units: 5 inches, 24 mph, 8C, 33%, etc.
Don't forget to identify the units and put them in there with the equations. Units often cancel out, leaving you with a unit for the answer. If the units don't cancel out correctly, that's an excellent indication that something is wrong in your setup.
Participation
includes attendance and promptness as well as traditional participatory
activities like asking questions, volunteering to put something on the board,
and laughing at my jokes.
From my point of view Quizzes and Exams are the least important part of the course. For whatever reason, students seem to place a great deal of importance on quizes and exams. Perhaps it is a high school thing. Perhaps students think that doing well on a test measures something above and beyond doing well on a test. In any event, I give exams and quizes from time to time. It seems to be what everybody expects from a mathematics course. The more you do the homework well, the fewer quizzes.