grid search is a hyperparameter tuning technique by trying pairs of all hyperparemeters sequentially

components

• a set of constituent objects
• an operation

requirements for group

• closed: if \(a,b \in G\), then \(a \cdot b \in G\)
• existence of identity: there is \(e \in G\) such that \(e\cdot a= a\cdot e = a\), for all \(a \in G\)
• existence of inverses: there is \(b \in G\) for all \(a \in G\) such that \(a\cdot b = b\cdot a = e\)
• associative: \((a\cdot b)\cdot c = a\cdot (b\cdot c)\) for all \(a,b,c \in G\)

additional information

identity in group commutates with everything (which is the only commutattion in groups

Notes on MATH 109, group theory.

Lectures

• SU-MATH109 SEP272023

PSets

These links are dead.

• SU-MATH109 Problem Set 1

Course logistics

• midterm: November 1st, final: December 14th, 8:30-11:30
• WIM assignment: December 8th, start of class (no late submissions)
• PSets: 8 in total, posted on Wednesdays at 8A, due following Tuesday at 8A

“Stuffing some stuff into buckets”

How many ways are there to sort \(n\) distinct objects to \(r\) buckets?

\begin{equation} r^{n} \end{equation}

grouping with entirely indistinct objects

You can simply reframe the grouping problem as permutation of the objects with \(r-1\) dividers along with your old \(n\) objects.

i.e.: sort this thing —

So:

\begin{equation} \frac{(n+r-1)!}{n! (r-1)!} \end{equation}

The Guilded Age is a period in history between 1877 and 1900. This period deepened divide in racism, deepened the split between poor and rich, and the fluidity of American social classes became more set in this time.

Links to Organize

• Imperialism
• New American South

Why is the “Guilded Age” “Guilded”?

Guilded: Outside Lined with Gold, Inside Contains Metal and is Less Valuable.

The Guilded Age consists of three different sections: