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Guided learning journeys that build knowledge step by step.
category · Learning · slug · learning · 7819 Paths
7819 Paths · page 740 / 782
This learning path introduces the geometric foundations of cartography, from basic map concepts to the mathematics of map projections. It covers spherical geometry, geodesy, coordinate systems, and the geometric transformations that underpin map projections, providing a clear understanding of how the 3D Earth is represented on 2D maps.
This learning path equips architecture and design students with the geometric knowledge needed to apply principles to architectural design and construction. It covers foundational geometry, structural geometry, tessellations, and the golden ratio, emphasizing practical applications in design.
This path covers the mathematical foundations and computational techniques for geometric modeling in CAD, including curve and surface representation, solid modeling, and applications. It progresses from linear algebra and computational geometry through Bézier curves, B-splines, NURBS, and solid modeling to practical CAD usage.
This learning path introduces core concepts and algorithms for computational geometry, including convex hulls, Voronoi diagrams, triangulations, and intersection detection. It builds on discrete mathematics and programming skills, with a focus on algorithmic thinking and practical implementation.
This advanced learning path guides graduate students in mathematics and physics through the foundations of Riemannian geometry, from smooth manifolds and tensor calculus to curvature and geodesics, culminating in applications to general relativity. It emphasizes the conceptual and computational links between differential geometry of surfaces, Riemannian metrics, connections, and curvature, providing a solid basis for further study in geometric analysis and theoretical physics.
This learning path guides graduate students from multivariable calculus and curve theory to a rigorous understanding of surface geometry, covering parameterization, fundamental forms, curvature, and geodesics. It emphasizes the conceptual dependencies and culminates in the Theorema Egregium and Gauss-Bonnet theorem.
A comprehensive learning path for university mathematics and physics students to understand the geometry of curves using differential calculus. It covers parametric curves, tangent vectors, curvature, torsion, and Frenet-Serret formulas, with necessary prerequisites in calculus and linear algebra.
This path guides university mathematics students through the foundations of hyperbolic geometry, focusing on the Poincaré disk model. Learners will explore hyperbolic lines, triangles, and key applications, building on Euclidean geometry and topology. The sequence progresses from essential prerequisites to advanced concepts, ensuring a coherent understanding of this non-Euclidean geometry.
This path introduces the core concepts of projective geometry, starting with the necessary linear algebra and analytic geometry prerequisites, then exploring the projective plane, points at infinity, projective transformations, and duality. It is designed for university mathematics students interested in the subject.
This learning path introduces the principles of spherical geometry, building from Euclidean geometry and trigonometry to the geometry of great circles, spherical triangles, and spherical excess, and culminating in practical applications such as area calculation on a sphere and navigation.