Collaborative Calculation and Data Science

colby

sagemath

github

google

cornellcollege

depaul

Calculate hydrogen energy levels using the Bohr equation (E = -13.6 eV/n²), visualize electron transitions, and generate electron configurations in this interactive quantum mechanics Jupyter notebook. Explore atomic physics from historical foundations to modern laser technology applications through Julia programming. CoCalc provides instant access to pre-configured Jupyter notebooks with Julia scientific tools, enabling focus on quantum concepts without software setup.

Master 3D molecular structure visualization using Python in CoCalc's collaborative environment. Build and analyze water, methane, and benzene molecules with VSEPR theory, calculate molecular properties, and assess drug-likeness using Lipinski's Rule. Interactive 3D visualizations, bond angle calculations, and structure-property relationships. Perfect for computational chemistry students learning molecular modeling and drug design fundamentals. No setup required in CoCalc.

Explore molecular orbital theory, VSEPR geometry, and bond energies through interactive R programming. Calculate lattice energies, predict molecular shapes, analyze electronegativity patterns, and apply quantum mechanical principles to real-world chemical systems. Comprehensive tutorial covering Lewis theory to modern computational chemistry applications in CoCalc's collaborative Jupyter environment.

Master multiple integration techniques through computational practice with double and triple integrals, change of variables, and Jacobian transformations. This interactive Jupyter notebook demonstrates integration over general regions, polar/spherical/cylindrical coordinates, and applications to mass, center of mass, and moments of inertia calculations. CoCalc's SageMath environment provides symbolic integration capabilities, region visualization tools, and numerical verification methods, enabling students to tackle complex multivariable integration problems with immediate visual feedback and computational support.

Master vector calculus fundamentals through interactive SageMath computations covering vector fields, gradients, and directional derivatives. This comprehensive Jupyter notebook introduces 3D coordinate systems, vector operations, and field visualizations with applications to fluid dynamics and electromagnetic fields. CoCalc's cloud-based platform provides instant access to symbolic computation tools and dynamic 3D plotting capabilities, enabling students to explore gradient fields, calculate divergence and curl, and understand vector calculus concepts through hands-on experimentation without software installation.

Discover the historical foundations of cell biology from Robert Hooke's cork cells (1665) through the development of cell theory in this interactive R-based Jupyter notebook. Explore milestone discoveries including Leeuwenhoek's animalcules, Schleiden and Schwann's cell theory, and Virchow's principle using data visualization and timeline analysis. CoCalc provides instant access to pre-configured R tools and ggplot2 for creating publication-quality historical timelines and impact assessments, enabling students to understand cellular discovery's 355-year journey without software setup.

Master ionic, covalent, and metallic bonding mechanisms through interactive R calculations. Analyze lattice energies, correlation patterns, and thermal stability relationships across diverse compounds from NaCl to Al₂O₃. Explore Born-Landé equation applications and electronegativity effects using computational chemistry tools in CoCalc's collaborative environment.

Explore van der Waals forces, hydrogen bonding, and ion-dipole interactions affecting boiling points and material properties. Analyze London dispersion forces, polarizability effects, and molecular weight correlations from noble gases to complex alcohols. Interactive R analysis reveals intermolecular force patterns in CoCalc.

Investigate prime factorization algorithms and unique factorization theorem using SageMath computational tools. Explore trial division, Pollard's rho method, and efficient factorization techniques for large integers. Interactive Jupyter notebook on CoCalc demonstrates fundamental theorem of arithmetic with step-by-step SageMath implementations and practical applications.

Complete advanced calculus applications including series, sequences, and differential equations using Julia's computational ecosystem. Explore convergence testing, Taylor series expansions, and numerical solutions to differential equations with DifferentialEquations.jl. Master parametric curves, polar coordinates, and multivariable calculus concepts while building practical programming skills for scientific computing applications in modern mathematical analysis and research environments.

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