Calculus
The branch of mathematics that studies rates of change (differentiation) and accumulated quantities (integration); its rigorization depends on the establishment of the concept of limits.
Timeline (last 90 days)
In calculus, making rigorous the idea of "adding up infinitely many infinitely small quantities to get a finite number" depended on establishing the concept of limits.
The calculus of Newton's and Leibniz's era used intuitive operations such as "dividing by zero" and "ghosts of departed quantities," practices that look non-rigorous today.
Acceleration is the derivative of velocity with respect to time, and velocity is the integral of acceleration with respect to time; in discrete systems this corresponds to numerical integration (such as the Euler or trapezoidal method), requiring handling of the sampling period, accumulated error and initial values.
The poster mentioned that when asked "if you have an acceleration equation, how do you find velocity" or "what is the integral of acceleration," everyone looked blank.
On the math side, Calculus I is one of the requirements, Calculus II is optional but helpful for understanding sequences; linear algebra only requires a basic level.
The dependency between linear algebra and calculus is very weak; it is entirely feasible to begin linear algebra immediately after building a solid precalculus foundation.
The mathematics underlying AI/ML is primarily concentrated in four areas: linear algebra, calculus, probability theory and statistics, and optimization theory.
The dependency between linear algebra and calculus is weak, allowing one to begin linear algebra in parallel immediately after establishing a pre-calculus foundation.
The mathematics required for deep learning is mainly concentrated in three areas: linear algebra, calculus, and probability theory.
The concepts of gradients and derivatives in calculus are essential tools for understanding optimization algorithms such as gradient descent.
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The mathematics required for deep learning is mainly concentrated in three areas: linear algebra, calculus, and probability theory.
60%UnverifiedIn calculus, making rigorous the idea of "adding up infinitely many infinitely small quantities to get a finite number" depended on establishing the concept of limits.
50%UnverifiedThe calculus of Newton's and Leibniz's era used intuitive operations such as "dividing by zero" and "ghosts of departed quantities," practices that look non-rigorous today.
50%UnverifiedAcceleration is the derivative of velocity with respect to time, and velocity is the integral of acceleration with respect to time; in discrete systems this corresponds to numerical integration (such as the Euler or trapezoidal method), requiring handling of the sampling period, accumulated error and initial values.
50%UnverifiedOn the math side, Calculus I is one of the requirements, Calculus II is optional but helpful for understanding sequences; linear algebra only requires a basic level.
50%UnverifiedThe dependency between linear algebra and calculus is very weak; it is entirely feasible to begin linear algebra immediately after building a solid precalculus foundation.
50%UnverifiedThe mathematics underlying AI/ML is primarily concentrated in four areas: linear algebra, calculus, probability theory and statistics, and optimization theory.
50%UnverifiedThe dependency between linear algebra and calculus is weak, allowing one to begin linear algebra in parallel immediately after establishing a pre-calculus foundation.
50%UnverifiedLinear algebra, probability theory, calculus, and optimization theory are the foundations for understanding how AI models work.
50%UnverifiedThe concepts of gradients and derivatives in calculus are essential tools for understanding optimization algorithms such as gradient descent.
50%Unverified微积分（特别是多元微积分和链式法则）直接驱动梯度下降这一核心优化算法
50%UnverifiedThe poster mentioned that when asked "if you have an acceleration equation, how do you find velocity" or "what is the integral of acceleration," everyone looked blank.
50%