[4.13.16] // 1:21 PM - day 16 / 100 days of productivity
It’s finally sunny! Still too cold to do work outside, but I compromised by working by the windows.
2025 on Tumblr: Trends That Defined the Year

Stranger Things
Sweet Seals For You, Always
Game of Thrones Daily
trying on a metaphor
todays bird
"I'm Dorothy Gale from Kansas"
Monterey Bay Aquarium

@theartofmadeline
let's talk about Bridgerton tea, my ask is open
Not today Justin
Xuebing Du
d e v o n
Keni

Andulka

One Nice Bug Per Day

Product Placement
seen from Guernsey

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@workhard-sleephard
[4.13.16] // 1:21 PM - day 16 / 100 days of productivity
It’s finally sunny! Still too cold to do work outside, but I compromised by working by the windows.

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9 April ~ notes for an ethics essay. I love when my subjects crossover because it makes it so easy haha (﹡ˆᴗˆ﹡) from my ig: instagram.com/studysthetics
10 • 04 • 2016 || Spanish studying for my last grammar test! After this two more test to go: one on writing and a mini interview.
Currently 📖✍🏼🍜
Going over anatomy in bed 📖

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Great way to start off the week! I’m really loving my new bullet journal layout. It’s going to be a homework heavy week, but I’m determined to get it all done!
Muji haul!
Unfortunate they had finished the sticky page flags and the glue, but I’m happy with my purchases. Those are 0.38 and 0.5 gel pens, I’m still trying to figure out which one is better for me.
02.17.16 || I’m studying geography for my test tomorrow, and I just love it so much! I don’t understand how people might find it “boring”
5 Things Every Student Should Do on Sunday Night
1. Check that nothing is due on Monday. Check again.
2. Write down due dates for the rest of the week.
3. Pack your bag. Phone, keys, everything.
4. Take a bath, have a long shower.
5. Pre-select outfits based on the weather

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Isomorphisms
Homomorphisms are functions that preserve structure in models.
However, it does not preserve elements of the models.
We do have a type of function that does preserve elements, a bijection.
We also want a slightly stronger version of the homomorphism, where things are related in one if and only if they are related in the other.
We call a bijective homomorphism an isomorphism
In a sense, this allows a much more natural way of saying two things have the “same” structure.
Since all statements about a structure are preserved under isomorphism, we can prove statements in one model, and move to another when the other model makes certain statements easier to work with.
Group isomorphisms:
Isomorphisms have allowed mathematicians to unify lots of different similarly behaving structures - numbers, symmetry, rotations, reärrangements, etc.
One isomorphism that revolutionized computation is the realization that isomorphism f(x)=e^x connects the group (R,+,0) and the group (R+,*,1).
It also allowed people to prove things about the roots of polynomials, that are made clearer when they become reärrangements.
In fact, over 100 mathematicians across the entire 20th Century worked on classifying all finite simple groups (the bits that combine to make any finite group). This means, if you take any finite simple group, there is an isomorphism to a group on that list.
Graph isomorphisms
Noticing an isomorphism between two different configurations of the Petersen graph makes the 3-fold and 5-fold symmetry the same.
In November 2015, László Babai announced an algorithm that finds if there is an isomorphism between two graphs in a much quicker method than the previous algorithms. His breakthrough in the field of graph isomorphisms might have implications for solving many extant problems in theoretical computer science.
Lineär Order isomorphisms:
It can be proved that there is an isomorphism between any two finite lineär orders.
But, extending this to infinite orders shows that this is not the case. However, there is a way to make a sequence of orders, such that any lineär order has an isomorphism to something in that sequence.
This order sequence allows us to nicely tame the many sizes of infinity, in a way.
22.03.2016 | Exam season is upon us
❝ motivation and success ❞
Some other snippets of my room ✨🌿

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having a terrible cold and doing swedish homework is not a great combo
*55/100 days of productivity* 12.3.16// Yoga at museum. Today I enjoyed the green park in Villa Pignatelli, practised my German reading der Spiegel literature magazine and had a relaxing yoga class. Now I’m going on with my Canetti reading, outside it’s cold and my blanket is warm and cozy. So happy!