Dear Aunt Sally 4.1

PEMDAS is an acronym widely taught in educational settings across the United States, serving as a mnemonic for remembering the Order of Operations in mathematical expressions. The components are:

• P (Parenthesis)
• E (Exponent)
• M (Multiplication)
• D (Division)
• A (Addition)
• S (Subtraction)

A popular adage associated with PEMDAS is "Please Excuse My Dear Aunt Sally," which highlights its relevance and familiarity among those studying mathematics. This application carries a playful nod to that tradition.

While computers—ranging from smartphone calculators to desktop PCs—are equipped to accurately interpret these expressions without user intervention, many users may wonder about the underlying algorithms that ensure correct results consistently. This application offers insight into one such algorithm, known as the Shunting Yard algorithm, created by Professor Edsger W. Dijkstra.

By delving into the mechanics of Order of Operations algorithms, this application caters to both programmers and students. For programmers, concepts such as queues and stacks serve as a reinforcement of prior computer science knowledge. For students, this platform enables them to input expressions and analyze them according to Order of Operations rules systematically. The Quiz mode generates random expressions based on user-defined lengths and magnitudes while validating the student's answers, allowing for a comprehensive review of incorrect responses through a step-by-step analysis.

The SOLVE mode permits users to enter algebraic expressions freely via an internal keyboard, which restricts entries to five fundamental mathematical operators (+, -, /, *, ^) and allows for one level of parenthesis. There is a limit of ten variables per expression, though no restrictions on their values apply.

In QUIZ mode, users can select between two and ten variables along with their maximum values and eligible operators. The application then generates random algebraic expressions based on these selected criteria.

Both modes feature an analysis page that guides users through the solution process, displaying Stack/Queue dynamics for enhanced understanding.