# Math Journal

I thought I’d make public my least readable of “articles”, which is nothing more than the daily notes on my journy as the World’s Oldest Math Major.

Monday, 12/11/2023:

Refine some precalc notes.

Calc I new course info notes.

Notes in Precalc OneDrive notes to examples in Paul’s Math Notes on Unit Circle (Calc Trig Review)

Begin notes on double and half-angle formulas proofs.

Tuesday, 12/12/2023

Continue viewing/notes on double and half-angle formula proofs. In OneNote, with summary in LaTeX here, in Double and Half-Angle Formulas.

Wednesday, 12/13/2023

Work on How to Use the Double and Half Angle Formulas for Trigonometry (Precalculus - Trigonometry 28)

Try paper + FriXion instead of Rocketbook

Discover and work with SchoolYourself

Thursday, December 14, 2023

Continue double and half angles.

Weekend December 16-17, 2023

Began looking at Graph theory, in Introductory Discrete Mathematics (which is not the right tool for that or much of anything).

Found this Playlist for Graph Theory with Python, and began on first couple of videos.

Last item from searching for a review of Introduction to Graph Theory, which looks quite good.

Monday December 18, 2023

Scanned earlier notes on double and half angles

Finished viewing Solving the Königsberg Bridge Problem with Python

Read sample of Introduction to Graph Theory.

Tuesday, December 19, 2023

Preview some Python Graph Libraries

Continue working through Graph Theory with Python videos.

Hack around some in igraph (in source/CodeSolid/GraphWork)

Wednesday, December 20, 2023

Learn about magic X method – something I saw Professor Leonard do. Watched this: Factoring Quadratics…How?. Also Intro to Solving Quadratics (Leonard Precalc # 16)

In source/CodeSolid/sympy-tutorial, review some SymPy stuff, in branch calculus_testing, file Precalc_Demo.ipynb. Especially figure out how to change aspect ratio. :)

Thurs Dec 21, 2023

Spent some time memorizing half-angle and double angle formulas. Flash cards. Have them down pretty well, needs more attempts.

Some Desmos – trying to figure out triangle tool. Not good. Also tried Geogebra.

Friday Dec 22, 2023

Do Board problems from this video. And watch parts. Do first 3 probls today, leave some for later.

Saturday Dec 23, 2023

Review Half Angle / Double Angle Formulas

Sunday, Dec 24, 2023 NocheBuena

Looking for History of Math – popular math books

Read about the Quadrature of the Lune, mentioned in Journey Through Genius

Play with parametric equations and curves,here and here; and on desmos

Tuesday, December 26, 2023

Using the vertical line test, to test if an equation etc is a function. Watch Logarthims - How?. This is a prelude to this, which I should do next time… Solving logarithmic equations See notes here.

Next watched part of this, Euler’s constant and natural log, but a bit too fast.

Wednesday 27 Dec 2023

More Log review

Thursday 28 Dec 2023

Begin watching Propositional Logic. Pretty much like intro to logic, but with new symbols and with mathematical formulae for truth operators.

Friday 29 Dec 2023

Reading How to Ace Calculus

LogReview.ipynb, reworking markdown Log notes with some Python.

Did some quadratic equation problems.

Began reading The Transcendental Tangle, “that awful book”.

Saturday 30 Dec 2023

Work on exponential growth and decay functions from Transcendental Tangle.

A bit puzzling why we need \(e\) for this, so maybe follow up in future with Exponential Growth and Decay (prof Leonard)

Sympy already there in online python on CodeSolid.

Sunday 31 Dec 2023

Begin Intro Graph Theory.

One easy rate of decay problem Python.

Monday 1 Jan 2024

Finish Graphs chapter of Trudeau’s Introduction to Graph Theory (No exercises yet, except mentally on the first two.). A great read.

Tuesday 2 Jan 2024

Continue Trudeau, on to planar graphs.

More on exponentials and logarithms. Resources in notes. Begin with this Graphs of Exponential Functions (Prof Leonard)

limits.py function to create limits.

Wednesday 3 Jan 2024

Continue on Trudeau, finish planar graphs, on to Euler’s function.

Thurs 4 Jan 2024

Work a bit on Euler’s formula (Trudeau ~ pp 101-104), and on paper.

More quadratic work, solve 10 chat-gpt-generated factorable quadratics using “diamond method”.

Friday 5 Jan 2024

Reading Trudeau

Same 10 quadratic fns from Thursday, this time using quad. formula.

Sat 1/6/24

Reading Trudeau - coloring.

Some exponentials with common base. (From this video)

Sun 1/7

Reading Trudeau only.

Monday 1/8

Tomorrow’s the day!

“Finish up” rough reading (no exercises and portions of difficult passages skipped) of Trudeau.

Intro to Solving Logarithms and Exponentials with, as usual, problems worked by hand.

Take mandatory “sign off on policy” brightspace quiz.

Tuesday, 1/9

First day of Calculus class, Calc I, MAT 271 with Emma Scothorn. “Rain” day, met virtually.

Finished about 60% or so of the math homework for this week. So far so good. Online (Cengage + Webassign) tools are pretty good. “Master It” button is your friend.

Weds, 1/10/2014

Lot of time (about 5 hours) spent on homework 2.3. (Need to do more problems 9, 11, and 12 especially).

New calculator came in, learned how to plot and do some basic things.

Thursday 1/11

First day in person Calc I Mat 271. Units 2.2 and 2.3 on limits (review – I was ahead on homework this week). Calculator skills awful for a test, so…

When I got home figured out how to substitute values into an equation, to solve functions, where the cubed kerjigger is, how to not use minus when I mean negative since the device is dumb, and a few other things along the way. Need about an hour a day to get good at this.

Friday 1/12

A smackerel of How to Ace Calculus

Redo in class exercises from Thursday, and problematic homework from section 2.3. Nice!

Begin working on Homework and reading for section 2.4. Good progress.

Begin Reading Robert Stoll’s Set Theory and Logic (sample)

Saturday 1/13/2024

Continue on Stoll’s Set Theory

About 40 minutes or so on homework # 2.4, Continuity and One-Sided Limits. Made some progress.

Sunday 1/14

Continue homework # 2.4. Only one thorny problem left and one to redo.

Continue a bit of Stoll’s Set Theory.

Monday 1/15

Troubleshot nasty problem from yesterday – first answer was almost correct, but wrote “log” instead of “ln” in the answer box. :(

About halfway done with problem set 2.5 – so more than a week ahead. :)

Associated video on infinite limits, etc.

Tuesday 1/16/24

Holiday - no class.

Begin 3.1 work

Wednesday 1/17/24

Continue work on exercises 3.1

Continue reading Stoll

Thursday 1/18/24

Attend class

Meet with teacher re # 2.5 # 5

Finish 3.1 homework and attendance this week. :)

Friday 1/19/24

Reading up on Coq

Download signature assignment, having trouble with files

Finally able to begin work on this signature assignment and pretty much finish it. It’s in OneDrive and can be edited further on Microsoft 365.

Saturday 1/20/24

Reading Boyer on history of math.

Reading Russell Introduction to Mathematical Philosophy; first intro to Peano’s axioms.

Sunday 1/21/24

Continue reading Boyer, enjoyed especially ~ pp. 51-52 on Pythagoreans and Euclid’s cool method for doing a golden section of a line segment, which he called finding the extreme and mean segment. Began some reading and playing around with regular solids, found the formula for the interior angles of any regular polygon, given n = number of sides, interior angle formula is as below: $\( \frac{(n - 2) * 180}{n} \)$

E.g. for a triangle, \(\frac{(3 - 2) * 180}{3} = \frac{180}{3} =60^o\)

For a square, \(\frac{(4 - 2) * 180}{4} = \frac{360}{4} = 90^o\)

For a regular pentagon, \(\frac{(5 - 2) * 180}{5}= \frac{540}{5} = \frac{540}{5} = 108^o\)

Monday, January 22, 2024

Continue reading Boyer.

Tuesday, 1/23/24

Class Calc I

Review previous homework, 2.2 and most of 2.3. Retry problems and build list of problem areas.

Continue Boyer.

Wed, 1/24/24

Lots of homework, 2.3 and finish 2.4. Revisit some problem areas.

Some reading of Boyer.

Thursday 1/25/24

Class

Section 2.5 review

Reading Euclid’s Elements (Casey)

Friday 1/26/24

Reading Euclid’s Elements (Casey)

Section 3.1 review

Did study guide as a practice exam. Got 14 done, believed OK. So maybe a 93. Need to look at again.

Saturday 1/27/24

Reading Euclid and Boyer

Plan math BA see Google sheets

Sunday

Reading Euclid

An easy proof (my “first”) of “the bisectors of supplemental angles are 90 degrees apart.”

Monday

Go over results of Study guide “exam” on Friday. Send corrections to Emma Scothorn.

Learn how to work problems involving giving the equation of the line at a point, assuming you have a function and need to find the tangent line at some x value.

Tuesday 1/30

Attend class

Meet with Emma Scothorn on misc issues.

Study for exam

Weds 1/31/24

Work through some problems in Larson, slope of line using def of deriv. Also work on some Intermediate Value Theorem problems.

Reading Boyer, also look up some conic section material, run into something called differential geometry – very cool.

Thursday 2/1

Exam Day Calc 1. Scored 103 of 100 points. Sweet.

Friday 2/2

Begin homework, studying next section.

Read Boyer

Saturday 2/3

Reading Boyer

Revisit MatPlotlib

Review some conic section basic equations

Sunday 2/4

Working in SymPy – more SymPy than math

Reading Clawson’s Mathematical Mysteries

Monday 2/5

Reading

Homework

Reading Calvin C. Clawson’s Mathematical Mysteries: The Beauty and Magic of Numbers. This is an and well-written (popular) overview of Number Theory.

Tuesday, 2/6

Class basic derivative rules

Homework

Reading Clawson

Wednesday 2/7

Begin homework on Product/Quotient rules – SLOW

Reading Clawson

Thursday 2/8

Class on Product and quotient rules and pos and velocity. Finish product/quotient homework. Nice!

Reading Clawson

Friday 2/9

Notebook for the article on Matplotlib for Book I Proposition I of the elements.

Reading Clawson

Saturday 2/10

Reviewing Chain Rule with Nancy Pi’s video. Work through the problems except last one, see notes.

Reading Clawson

Sunday 2/11

Light on math per se :( – just working on Symplot idea (SymPy simplified Matplotlib plotting)

Monday 2/12

Reading Clawson

Homework on chain rule. About 10 out of 17 problems

Tuesday 2/13

Class - chain rule.

Finish 1/2 homework for next week, chain rule problems. (Webassign 3.4)

Wednesday 2/14

Some reading in Stoll

Work on 3.5 webassign and review some implicit derivative videos.

Thursday 2/15

Class – Implicit differentiation

Boyer reading, plus reading up on synthetic division, Horner’s method, and lattice multiplication. Neat.

Homework 3.5 webassign, still more to do. Headache. :(

Friday 2/16

Finish WebAssign Homework

Saturday 2/17

Reading Boyer History of Mathematics

Sunday, 2/18

Reading Boyer History of Mathematics

Monday, 2/19

Reading Boyer History of Mathematics

Learning about Derivatives of Inverse Functions and elsewhere, and next few videos.

2/3 (so far) of Webassign 3.6 homework for Calc I.

Tuesday 2/20

Class on differentials of inverses, inverse trig fns.

Finish homework for that class

Reading Boyer History of Mathematics

Wednesday 2/21

Begin working on related rates – viewing only so far

Reading Boyer History of Mathematics

Note: Here there was a big hiatus in entries, though not in Math, for several days (until 3/3). On 3/3/24 I caught up.

Thurday 2/22

Class

Finish up related rates problems

Reading Boyer

Friday 2/23

Work on Test 2 Study guide Calc 1

Somewhere in here began “What is Mathematics”

Boyer

Saturday 2/24

Boyer and What is Math

Sunday 2/25

Boyer and What is Math

Monday 2/26

More studying for Calc 1 test 2

Reading Boyer

Tuesday 2/27

Class – review for test 2

Study for test

Boyer

Wednesday 2/28

Final studying for test

Thursday 2/29

Calc 1 test 2. Got a grade of 102/100 with bonus question. :) !!!

Friday 3/1

Reading Boyer History of Math

Saturday 3/2

Reading Boyer History of Math

Sunday 3/3

Reading Boyer History of Math

Monday 3/4

Reading Boyer History of Math

Article on Taking Calculus in your sixties

Tuesday 3/5

Reading Boyer History of Math

Finish article

Begin Viewing Calc One Lecture 4.1 Professor Leonard on Antiderivatives & Integration

Wednesday 3/6

Reading Boyer

Viewing Calc One Lecture 4.1 (several parts)

Thursday 3/7

Reading Boyer

Reading on series, infinite series, Wikipedia on Taylor Series etc. Scratching the surface.

Friday 3/8

Reading Boyer

Saturday 3/9

Reading Boyer

Organize Calc I notes (Ok, that’s minor!)

Sunday 3/10

Reading Boyer

Monday 3/11

Reading Boyer

Get started on topics for homework due. Extrema on an Interval, Rolle’s Theorem and MVT, Increasing and Decreasing Functions and First Derivative Test. Start with this one: https://www.youtube.com/watch?v=V239IIoGVT8.

Tuesday 3/12

Class – extrema

Finish 4.1 homework, most of 4.2

Reading Boyer

Wednesday 3/13

Reading Boyer

Some “What is Math” (not a lot)

Work on 4.3

**************** GAP ****************** With frowny face: :( **************** GAP ******************

Monday, 3/25

OK, let’s not even try to fill in that 12 day gap in any day-by-day way. Twelve days! That’s bad. But here are some highlights from that period:

I’m primarily working on What Is Math now, having finished Boyer

Friday and over the weekend of 3/23-3/24 I did some more Logarithm review. It seems I need to do that every few months, or just work a big plate of problems until I have completely internalized them. I may need to break down and write an article on them.

Continuing with Homework / classes for Calculus I, of course.

Began an article on exploring basic number theory with Python.

Another gap filled in 3-25 to 4-1

Tues, 3/26

Class. Around here begin sweating the load on Exam 3

Study for Exam 3

Weds 3/27

Study for Exam 3

Reading Courant.

Thurs 3/28

Class. Study for exam 3 in Calc 1

Reading Courant.

Friday 3/29

Study for exam 3 in Calc 1

Homework

Reading Courant.

Sat 3/30

Study for exam 3 in Calc 1

Homework and Lab

Reading Courant.

Sunday 3/31

Study for exam 3 in Calc 1

Reading Courant.

Monday, 4/1

Study for Exam 3

Reading Courant.

Tuesday 4/2

Exam 3. Hardest yet

Catch up math journal