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.

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.

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.

Discover the foundation of calculus through limits and continuity concepts using Julia programming. Master the epsilon-delta definition, squeeze theorem, and essential limits like sin(x)/x approaching 1. Explore numerical verification techniques with ForwardDiff.jl and visualize limit behavior through interactive plots. Perfect introduction to computational calculus combining mathematical rigor with modern programming tools in CoCalc's collaborative environment.

Master derivative fundamentals and instantaneous rate of change using Julia's symbolic and numerical capabilities. Learn the definition of derivatives as limits of difference quotients, apply power rule, chain rule, and product rule through practical examples. Explore motion analysis connecting position, velocity, and acceleration while utilizing ForwardDiff.jl for automatic differentiation and SymPy for exact symbolic computation in physics applications.

Apply calculus to optimization problems and critical point analysis using Julia's symbolic and numerical tools. Master finding extrema, inflection points, and applying the second derivative test for function behavior analysis. Solve real-world optimization scenarios including material usage minimization and projectile motion range maximization. Utilize SymPy for exact solutions and Plots.jl for visualizing optimization landscapes in educational contexts.

Master calculus fundamentals through hands-on Julia programming with comprehensive coverage of limits, derivatives, and integrals. Learn instantaneous rate of change, optimization techniques, and the Fundamental Theorem of Calculus while building computational skills in numerical differentiation and integration. Interactive CoCalc environment provides symbolic computation capabilities with SymPy, powerful plotting with Plots.jl, and real-world applications in physics and engineering optimization problems.

Explore advanced differentiation techniques and applications using Julia's computational power. Master implicit differentiation, logarithmic differentiation, and related rates problems with real-world engineering scenarios. Learn L'Hôpital's rule for indeterminate forms while building proficiency in symbolic manipulation through SymPy integration. Interactive visualizations demonstrate tangent lines and derivative behavior in CoCalc's collaborative mathematical computing environment.

Master integration fundamentals and the Fundamental Theorem of Calculus through Julia programming. Learn definite and indefinite integrals, substitution methods, and integration by parts using symbolic computation. Explore numerical integration techniques including trapezoidal rule and Simpson's rule with QuadGK.jl for high-precision calculations. Apply integrals to physics problems calculating work, area under curves, and accumulated quantities in engineering contexts.

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.

Project: Publications

Public Paths

Product

Resources

Company