Prerequisite Diagnostics

Prerequisite Diagnostics & Targeted Review Plan

Assess Python fundamentals and mathematics intuition to identify gaps, verify skip eligibility, and schedule targeted reviews into planned review days.

Review items are scheduled into planned weekly review days (Day 07 / Day 14, 480 min budget each). Total mandatory curriculum hours remain exactly 720 hours.

Prior Knowledge & Skip Requests

Selecting a skip option without passing an independent diagnostic does not certify mastery. All skip recommendations require demonstrated evidence.

I have extensive Python background and request skip consideration for Days 01-03 I have college-level mathematics background and request skip consideration for Days 16-18

Mode Independent Diagnostic Check (No AI assistance) Agent-assisted practice

py_mutability python_fundamentals

Question 1: Python Object Identity & In-Place Mutability

In Python, when executing the following snippet:

a = [1, 2, 3]
b = a
b.append(4)

What is the value of a and what is the underlying memory reason?

A. `a` is `[1, 2, 3]`; assignment `b = a` copies the list contents into a new object. B. `a` is `[1, 2, 3, 4]`; `b` and `a` reference the same mutable list object on the heap, so in-place mutation alters the shared object. C. `a` is `[1, 2, 3]`; mutating `b` creates a copy-on-write duplicate automatically. D. A `TypeError` is raised because list identifiers cannot be rebound.

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py_control_scope python_fundamentals

Question 2: Function Scope, State & Pure Functions

When structuring code for autograd or machine learning pipelines, why are pure functions (functions whose outputs depend only on explicit arguments and do not mutate global variables) strongly preferred?

A. Pure functions execute ten times faster because Python disables garbage collection inside them. B. Pure functions eliminate hidden state mutations and side effects, making gradient traces, backpropagation, and minimal reproducible examples deterministic and easily testable. C. Python compilers reject any function that references or reassigns an outer scope variable. D. Pure functions do not require memory allocation on the call stack.

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math_calculus_derivatives math_foundations

Question 3: Derivatives, Tangent Lines & Gradient Intuition

For a loss function $L(w) = w^2 - 4w + 4$, the derivative is $L'(w) = 2w - 4$. If current parameter is $w = 3$, what is $L'(3)$ and how should $w$ be updated to reduce loss?

A. $L'(3) = -2$; because slope is negative, increase $w$ by adding a positive step. B. $L'(3) = +2$; because slope is positive, moving in the negative gradient direction requires decreasing $w$ ($w \leftarrow w - \eta \cdot 2$). C. $L'(3) = 0$; the loss is already at its minimum value. D. $L'(3) = +5$; multiply the parameter by 3 to reach the origin.

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math_linear_algebra_tensors math_foundations

Question 4: Linear Algebra, Matrix Dimensions & Layer Accounting

In a neural network linear layer $Y = XW$, input batch $X$ has shape $(32, 128)$ and output $Y$ must have shape $(32, 64)$. What must the shape of parameter matrix $W$ be?

A. Shape $(32, 64)$, matching batch size and target output dimension. B. Shape $(128, 64)$, matching inner dimension 128 to aggregate feature dot products and producing 64 output features. C. Shape $(64, 128)$, transposing outputs into batch dimensions. D. Shape $(32, 128)$, matching the input tensor shape exactly.

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math_probability_loss math_foundations

Question 5: Probability, Log-Likelihood & Cross-Entropy

In classification, why does cross-entropy loss $-\log(p_{\text{true}})$ penalize a prediction of $p_{\text{true}} = 0.01$ exponentially more than $p_{\text{true}} = 0.50$?

A. Because cross-entropy truncates small values to NaN. B. Because $-\log(x)$ approaches infinity as $x \to 0$, providing steep gradients to correct overconfident erroneous predictions. C. Because probabilities are squared before computing logarithms in modern deep learning. D. Because negative signs invert the numerical precision of floating-point representations.

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