--Docker--
Dockerfile for a Go project

FROM golang:1.15 AS builder

RUN apt update && apt upgrade -y && \

apt install -y git \

WORKDIR /app

# Get install script, run, and make binary

RUN curl -fLo install.sh https://raw.githubusercontent.com/cosmtrek/air/master/install.sh \

&& chmod +x install.sh && sh install.sh && cp ./bin/air /bin/air

• Always combine RUN apt-get update with apt-get install in the same RUN statement as suggested in the Dockerfile best practices under the 'apt-get' section here: https://docs.docker.com/develop/develop-images/dockerfile_best-practices/
• The WORKDIR command is used to define the working directory of a Docker container. Any RUN, CMD, ADD, COPY, or ENTRYPOINT command will be executed in the specified working directory.

apt vs. apt-get

• apt is a subset of apt-get and apt is usually preferred
• apt provides all the necessary commands for package management so just go with that

apt update vs. apt upgrade

• apt update updates the list of available packages and their versions, but it does not install or upgrade any packages.
• apt upgrade actually installs newer versions of the packages you have. After updating the lists
• -y flag means "say yes to all"
• https://askubuntu.com/questions/94102/what-is-the-difference-between-apt-get-update-and-upgrade

--C++ basics--

Generics in C++

#include <iostream>

using namespace std;

template <class T>

T GetMax (T a, T b) {

T result;

result = (a>b)? a : b;

return (result);

}

int main () {

int i=5, j=6, k;

long l=10, m=5, n;

k=GetMax<int>(i,j);

n=GetMax<long>(l,m);

cout << k << endl;

cout << n << endl;

return 0;

}

• Templates in C++: https://www.cplusplus.com/doc/oldtutorial/templates/

Logical data structures—implemented using physical data structures: arrays or linked lists

• Stack (linear, LIFO)
• Queues (linear, FIFO)
• Trees (non-linear)
• Graph (non-linear)
• Hash Table (tabular)

Abstract Data Type (ADT)

• ADT is a type (or class) for objects whose behavior is defined by a set of value and a set of operations
• The definition of ADT only describes what operations are to be performed but not how these operations will be implemented, making it abstract
• List, Stack, & Queue ADTs: https://www.geeksforgeeks.org/abstract-data-types/

--Discrete Math--

Math Theorem Example: an even integer plus an odd integer is another odd integer

Proof:

• Suppose m is even and n is odd (1. State the assumptions)
• ∃k1 ∈ Z and ∃k2 ∈ Z so that m = 2k1 and n=2k2 + 1 (2. Formally define the assumptions)
• Then, m + n = (2k1) + (2k2+1) = 2(k1+k2) + 1. Let k3 = k1 + k2, and note it is an integer. (3. Manipulation)
• Hence ∃k3 ∈ Z so that m + n = 2k3 + 1 (4. Arrive at definition of conclusion)
• Thus m + n is odd (5. Conclusion)

Divisibility

• For n and d integers, d ≠ 0, d | n ↔ if ∃k ∈ Z such that n = dk
• When we say d | n, it means n is divisible by d

∀x ∈ D, P(x) → Q(x) where we quantify with specific x values, it uses a single arrow to show implication between two statements

P(x) ⇒ Q(x) with a double arrow is an implication between two predicates; it means the same thing as above

Other Proof Methods:

• Disproving with Counterexamples
• Proof by division into cases
• Proof by contradiction
• Proof by contrapositive