Across
- 3. Algebraic structure defined by a single associative operation and an identity element, essential in abstract algebra
- 5. Space that locally resembles Euclidean geometry but globally exhibits complex topological properties
- 8. Mathematician who established deep connections between symmetries and conservation principles in theoretical physics
- 9. Topological map where each base point corresponds to a fiber, facilitating projection from higher-dimensional spaces
- 11. Algebraic system with two operations, adhering to specific axiomatic constraints, fundamental in abstract algebra
- 12. Field studying properties preserved under continuous deformation, revealing fundamental characteristics of spatial forms
- 15. Differential operator quantifying how a function deviates from its local average, pivotal in PDEs and harmonic functions
- 16. Multi-dimensional array generalizing scalars and vectors, capturing complex multilinear relationships
Down
- 1. Point at which a function's behavior becomes undefined or infinite, often analyzed using contour integrals
- 2. Measure of the strength and direction of the linear relationship between two variables, adjusted for their means
- 4. Scalar in matrix analysis reflecting stretching or shrinking, embedded within characteristic polynomial roots
- 6. Operator aggregating infinitesimal elements to determine total accumulation or area under a curve
- 7. Bijective mapping preserving the algebraic structure, ensuring equivalence between seemingly different systems
- 10. Point where a system's qualitative behavior bifurcates into distinct regimes, often analyzed in dynamical systems
- 13. Vector field derived from partial derivatives, indicating the maximal rate of increase in a function's value
- 14. Minimal set of linearly independent vectors spanning a vector space, providing a coordinate system for all elements