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This study aims to analyze the derivatives of a two-variable function and visualize the results in the form of a 3D graph using Python. Derivatives of two-variable functions are essential in multivariate analysis, such as optimization and surface analysis. The study uses Visual Studio Code as the Integrated Development Environment (IDE) to develop and run Python code, utilizing libraries such as NumPy, SymPy, and Matplotlib for mathematical computations and visualization. The first step involves programming partial derivatives of a two-variable function using SymPy. Subsequently, the derivative results are visualized in 3D using Matplotlib to illustrate the surface and gradient of the function. The goal of this research is to provide a deeper understanding of the application of derivatives in two-variable functions and the benefits of visualization in analyzing these derivative results. The findings are expected to contribute to the fields of mathematics education and numerical computation applications.

Algorithms are at the core of computer science and play an important role in computer programming. Programming aims to tell the computer to perform certain functions. Computer instructions provide a set of instructions written in a language that the computer can understand. Programming algorithms consist of various detailed sequential steps aimed at solving various computer programming problems. A computer is an electronic device capable of receiving, processing, storing and creating information. In general, a computer is a machine that is used to perform various tasks, such as data processing, calculations, storing information, and executing predefined programs. Computers are divided into two parts, namely hardware and software which work together to support various types of computers and applications. Some applications of algorithms in computer science learning are data compression algorithms, binary search algorithms, linear search algorithms, repetition algorithms and hashing algorithms. When writing and creating an algorithm, you don't really focus on the programming language, so there are lots of algorithms used in programming. The purpose of this scientific work is to find out how important it is to apply programming algorithms in computer science learning. In order to achieve this goal, a literature study research method was carried out.

An algorithm is an effective method or steps arranged in writing and sequentially containing a collection of commands to solve a problem. Every problem must be resolved logistically, systematically and organized. Programming is a process that allows computers to solve or solve problems in the form of solving steps, as done in programming code languages, so that computers can actually solve problems. A programming algorithm is a systematic collection of steps aimed at solving any computer programming problem. Based on the writing format, the application of the programming algorithm is descriptive, pseudocode, and flowchart. And the basic structure of a programming algorithm can be used in three forms: sequence, selection, and repetition. Algorithm writing is not governed by any particular rules; however, each step of the algorithm must have a clear goal. The purpose of writing this article is to study the functions and various implementations of programming algorithms and their applications in everyday life. To achieve this goal, this article was written using the literature study method, which means reading systematically and in an organized manner books, journals and other sources related to programming algorithms. Programming algorithms have many very important functions. Solving a problem is the main function of a programming algorithm. Algorithms function to simplify programs, make it easier to find errors, and minimize repetitive program writing. Programming algorithms also have implementations and functions for us in everyday life. Examples of algorithms in our daily activities, such as installing applications, sending emails, receiving payments at ATMs, making fried noodles, making cakes, making coffee, riding motorbikes, cooking rice, etc.

Complex mathematics is one branch of the many existing mathematics, where complex mathematics itself discusses and studies complex numbers. Complex numbers are divided into two, namely the real part and the imaginary part. Meanwhile, a programming algorithm is a collection of steps that have a structured nature to solve problems and tasks in the form of programming to achieve certain goals. Programming algorithms can design efficient solutions to various challenges. Utilizing programming algorithms requires logical thinking, to analyze problems in as much detail as possible with in-depth understanding in order to get the desired results. This article uses a literature study method with qualitative research to find out how to solve complex mathematical problems using numerical programming algorithms. This article also aims to explain the close relationship between complex mathematics and numerical programming algorithms as a form of problem solving. In programming algorithms code is needed as a representation of complex numbers, in complex mathematics it also helps to understand how to store and manipulate and form program code.