Dear Aunt Sally vs EigenAlpha

PEMDAS is an acronym that is taught in school classrooms across the nation. It helps students remember the priority, or Order of Operations, used to solve expressions involving strings of numbers and operators. It stands for: P(arenthesis) E(xponent) M(ultiplication) D(ivision) A(ddition) S(ubtraction) A familiar mnemonic widely used in place of PEMDAS is: Please Excuse My Dear Aunt Sally. Thus the name of this application... Kind of an inside joke for the mathematical types. Computers, including smart phone calculators, desktops, etc. have built in functionality to properly interpret such expressions so we don't have to. But have you ever wondered what algorithms the CPU executes to get the right answer every time? This app demonstrates one such algorithm called the Shunt Yard, developed a few years back by Professor Edsger W. Dijkstra. We’re going to take a closer look under the hood at Order of Operations algorithms. It will interest programmers and school students alike; for programmers, the use of queues and stacks will reinforce previous computer science learning; for students, it allows them to write an expression, then analyze it using Order of Operations rules, step by step. The Quiz mode generates random expressions of user selected lengths and magnitudes and checks the student's answer. Incorrect answers can be examined using the same step by step process. In the SOLVE mode, algebraic expressions are entered free hand using an internal keyboard which limits entries to the five common mathematical operators (+ - / * ^) as well as one level of parenthesis. There is a maximum term limit of ten variables, but no limit to their magnitude in this mode. In the QUIZ mode, between two and ten variables can be selected, their maximum value and which operators that are eligible. The program then randomly generates an algebraic expression using these parameters. Both modes make available an analysis page which is used to step through the solution. Stack/Queue dynamics are displayed.

EigenAlpha: Linear Algebra Core Skills Training Unlock the visual and spatial power of Linear Algebra. EigenAlpha is an interactive learning console designed for university students, engineers, and machine learning enthusiasts who want to develop a deep, intuitive, and mathematical grasp of vector spaces, matrices, and linear mappings. Skip rote memorization. EigenAlpha combines structured curriculum progression with stunning visual diagnostics to help you bridge the gap between abstract equations and geometric transformations. KEY FEATURES: Structured Course Progression: Move step-by-step through core Linear Algebra units—from basis vector spans and matrix dimensions to QR decompositions, eigenvalues, and Gram-Schmidt orthogonalization. Macro Skill Diagnostics: View your real-time accuracy across 6 core mathematical domains, including Matrix Arithmetic, Algorithmic Reduction (Gaussian Elimination), Spectral Decomposition, and Invariant Inspection. Applied Crossover Case Studies: Explore how abstract matrix concepts drive state-of-the-art modern technologies. Follow step-by-step reasoning progressions for real-world scenarios, including Google PageRank spectral convergence. Conceptual Diagrams & Pitfalls: Review custom high-contrast visuals mapping out transformations and eigenvalues. Learn to bypass common pitfalls and exam tips carefully curated by math researchers. Reset & Restore Control: Maintain full command over your learning log. Reset diagnostic progress to re-test your accuracy, and easily restore premium license entitlements across all your iOS devices. Accessibility Integrated: Fully optimized for Dynamic Type font scaling and screen reader VoiceOver narration. WHO IS IT FOR? - STEM Undergrads: Excel in college-level Linear Algebra courses and diagnostic exams. - AI & Machine Learning Developers: Understand the vector transformations, dimension spaces, and spectral decomposition behind neural networks and PCA. - 3D Developers & Graphics Engineers: Master translation, rotation, and projection matrices.