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Ergodic Theory

Ergodic theory deals with the study of invariant measures in dynamical systems. "Measures" are generalizations of concepts such as length, area, volume, etc. "Invariant measures" are measures that are preserved by functions. "Dynamical systems" are systems in which a fixed rule governs the time dependence of points in a geometric space, such as the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish in a lake each spring.

An introductory class in ergodic theory is likely to include the following topics:

  • Measure-preserving transformations
  • Isomorphism, conjugacy, and spectral isomorphism
  • Measure-preserving transformations with discrete spectrum
  • Entropy
  • Topological dynamics
  • Invariant measures for continuous transformations
  • Topological entropy
  • Relationship between topological entropy and measure-theoretic entropy
  • Topological pressure and its relationship with invariant measures


There is no lack of books on this interesting mathematical topic, some of which can be seen on Amazon.com or Google. In addition, students should spend time with the journal of Ergodic Theory and Dynamical Systems, put out by Cambridge Journals Online.

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      • Illuminate\Database\Events\QueryExecuted (1.57ms)
      • Illuminate\Cache\Events\CacheMissed (225μs)
      • Illuminate\Cache\Events\CacheMissed (82μs)
      • Illuminate\Database\Events\StatementPrepared (1.72ms)
      • Illuminate\Database\Events\QueryExecuted (8.04ms)
      • eloquent.retrieved: App\Models\Subject (438μs)
      • eloquent.retrieved: App\Models\Subject (39μs)
      • eloquent.retrieved: App\Models\Subject (55μs)
      • eloquent.retrieved: App\Models\Subject (1.76ms)
      • eloquent.retrieved: App\Models\Subject (16μs)
      • eloquent.retrieved: App\Models\Subject (14μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (12μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • Illuminate\Database\Events\StatementPrepared (1.21ms)
      • Illuminate\Database\Events\QueryExecuted (1.83ms)
      • eloquent.retrieved: App\Models\SubjectCat (6.78ms)
      • eloquent.retrieved: App\Models\SubjectCat (367μs)
      • eloquent.retrieved: App\Models\SubjectCat (30μs)
      • Illuminate\Cache\Events\KeyWritten (14.14ms)
      • Illuminate\Cache\Events\KeyWritten (1.65ms)
      • Illuminate\Cache\Events\CacheHit (12.91ms)
      • Illuminate\Cache\Events\CacheHit (1.09ms)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (638μs)
      • Illuminate\Cache\Events\CacheHit (268μs)
      • Illuminate\Cache\Events\CacheHit (353μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (444μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (334μs)
      • Illuminate\Cache\Events\CacheHit (217μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (264μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (447μs)
      • Illuminate\Cache\Events\CacheHit (5.01ms)
      • Illuminate\Cache\Events\CacheHit (310μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (296μs)
      • Illuminate\Cache\Events\CacheHit (201μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (216μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (5.41ms)
      • Illuminate\Cache\Events\CacheHit (417μs)
      • Illuminate\Cache\Events\CacheHit (315μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (457μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (382μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (229μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (362μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (345μs)
      • Illuminate\Cache\Events\CacheHit (373μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (186μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (247μs)
      • Illuminate\Cache\Events\CacheHit (202μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (249μs)
      • Illuminate\Cache\Events\CacheHit (176μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (7.58ms)
      • Illuminate\Cache\Events\CacheHit (284μs)
      • creating: components.tutors-card (2.32ms)
      • composing: components.tutors-card (198μs)
      • Illuminate\Database\Events\StatementPrepared (2.52ms)
      • Illuminate\Database\Events\QueryExecuted (7.51ms)
      • Illuminate\Cache\Events\CacheMissed (232μs)
      • Illuminate\Cache\Events\CacheMissed (97μs)
      • Illuminate\Database\Events\StatementPrepared (4.65ms)
      • Illuminate\Database\Events\QueryExecuted (6.71ms)
      • eloquent.retrieved: App\Models\Subject (110μs)
      • eloquent.retrieved: App\Models\Subject (19μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (12μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • Illuminate\Database\Events\StatementPrepared (1.65ms)
      • Illuminate\Database\Events\QueryExecuted (1.64ms)
      • eloquent.retrieved: App\Models\SubjectCat (96μs)
      • eloquent.retrieved: App\Models\SubjectCat (21μs)
      • eloquent.retrieved: App\Models\SubjectCat (12μs)
      • eloquent.retrieved: App\Models\SubjectCat (10μs)
      • Illuminate\Cache\Events\KeyWritten (6.15ms)
      • Illuminate\Cache\Events\KeyWritten (1.36ms)
      • Illuminate\Cache\Events\CacheHit (7ms)
      • Illuminate\Cache\Events\CacheHit (723μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (301μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (173μs)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (250μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (243μs)
      • Illuminate\Cache\Events\CacheHit (212μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (441μs)
      • Illuminate\Cache\Events\CacheHit (262μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (269μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (1.49ms)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (273μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (1.24ms)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (287μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (2.03ms)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (336μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • Illuminate\Cache\Events\CacheHit (195μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (2.02ms)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (277μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (245μs)
      • Illuminate\Cache\Events\CacheHit (233μs)
      • Illuminate\Cache\Events\CacheHit (261μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (206μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (406μs)
      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (227μs)
      • Illuminate\Cache\Events\CacheHit (197μs)
      • Illuminate\Cache\Events\CacheHit (308μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (317μs)
      • Illuminate\Cache\Events\CacheHit (369μs)
      • Illuminate\Cache\Events\CacheHit (236μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (401μs)
      • Illuminate\Cache\Events\CacheHit (344μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (297μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (162μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (179μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (251μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (208μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • creating: components.tutors-card (880μs)
      • composing: components.tutors-card (58μs)
      • Illuminate\Database\Events\StatementPrepared (1.1ms)
      • Illuminate\Database\Events\QueryExecuted (1.2ms)
      • Illuminate\Cache\Events\CacheMissed (376μs)
      • Illuminate\Cache\Events\CacheMissed (118μs)
      • Illuminate\Database\Events\StatementPrepared (2.95ms)
      • Illuminate\Database\Events\QueryExecuted (10.59ms)
      • eloquent.retrieved: App\Models\Subject (162μs)
      • eloquent.retrieved: App\Models\Subject (22μs)
      • eloquent.retrieved: App\Models\Subject (12μs)
      • eloquent.retrieved: App\Models\Subject (11μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (7μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (10μs)
      • eloquent.retrieved: App\Models\Subject (8μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • eloquent.retrieved: App\Models\Subject (9μs)
      • Illuminate\Database\Events\StatementPrepared (832μs)
      • Illuminate\Database\Events\QueryExecuted (893μs)
      • eloquent.retrieved: App\Models\SubjectCat (88μs)
      • eloquent.retrieved: App\Models\SubjectCat (19μs)
      • Illuminate\Cache\Events\KeyWritten (2.91ms)
      • Illuminate\Cache\Events\KeyWritten (753μs)
      • Illuminate\Cache\Events\CacheHit (2.75ms)
      • Illuminate\Cache\Events\CacheHit (1.05ms)
      • Illuminate\Cache\Events\CacheHit (892μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (240μs)
      • Illuminate\Cache\Events\CacheHit (350μs)
      • Illuminate\Cache\Events\CacheHit (258μs)
      • Illuminate\Cache\Events\CacheHit (226μs)
      • Illuminate\Cache\Events\CacheHit (421μs)
      • Illuminate\Cache\Events\CacheHit (220μs)
      • Illuminate\Cache\Events\CacheHit (213μs)
      • Illuminate\Cache\Events\CacheHit (8.3ms)
      • Illuminate\Cache\Events\CacheHit (278μs)
      • Illuminate\Cache\Events\CacheHit (239μs)
      • Illuminate\Cache\Events\CacheHit (177μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • Illuminate\Cache\Events\CacheHit (154μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (405μs)
      • Illuminate\Cache\Events\CacheHit (232μs)
      • Illuminate\Cache\Events\CacheHit (152μs)
      • Illuminate\Cache\Events\CacheHit (167μs)
      • Illuminate\Cache\Events\CacheHit (142μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (148μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (160μs)
      • Illuminate\Cache\Events\CacheHit (178μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (498μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (394μs)
      • Illuminate\Cache\Events\CacheHit (347μs)
      • Illuminate\Cache\Events\CacheHit (161μs)
      • Illuminate\Cache\Events\CacheHit (221μs)
      • Illuminate\Cache\Events\CacheHit (163μs)
      • Illuminate\Cache\Events\CacheHit (332μs)
      • Illuminate\Cache\Events\CacheHit (3ms)
      • Illuminate\Cache\Events\CacheHit (235μs)
      • Illuminate\Cache\Events\CacheHit (315μs)
      • Illuminate\Cache\Events\CacheHit (230μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • creating: components.tutors-card (680μs)
      • composing: components.tutors-card (60μs)
      • Illuminate\Database\Events\StatementPrepared (1.04ms)
      • Illuminate\Database\Events\QueryExecuted (2.76ms)
      • Illuminate\Cache\Events\CacheHit (3.72ms)
      • Illuminate\Cache\Events\CacheHit (16.41ms)
      • Illuminate\Cache\Events\CacheHit (577μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (182μs)
      • Illuminate\Cache\Events\CacheHit (147μs)
      • Illuminate\Cache\Events\CacheHit (10.61ms)
      • Illuminate\Cache\Events\CacheHit (186μs)
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      • Illuminate\Cache\Events\CacheHit (172μs)
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      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • Illuminate\Cache\Events\CacheHit (168μs)
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      • Illuminate\Cache\Events\CacheHit (198μs)
      • Illuminate\Cache\Events\CacheHit (228μs)
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      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (165μs)
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      • Illuminate\Cache\Events\CacheHit (160μs)
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      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (215μs)
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      • Illuminate\Cache\Events\CacheHit (281μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (193μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (187μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (387μs)
      • Illuminate\Cache\Events\CacheHit (170μs)
      • Illuminate\Cache\Events\CacheHit (276μs)
      • Illuminate\Cache\Events\CacheHit (8.31ms)
      • Illuminate\Cache\Events\CacheHit (304μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (360μs)
      • Illuminate\Cache\Events\CacheHit (346μs)
      • Illuminate\Cache\Events\CacheHit (238μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (348μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (185μs)
      • Illuminate\Cache\Events\CacheHit (164μs)
      • Illuminate\Cache\Events\CacheHit (260μs)
      • Illuminate\Cache\Events\CacheHit (418μs)
      • Illuminate\Cache\Events\CacheHit (214μs)
      • Illuminate\Cache\Events\CacheHit (274μs)
      • Illuminate\Cache\Events\CacheHit (8.25ms)
      • Illuminate\Cache\Events\CacheHit (348μs)
      • Illuminate\Cache\Events\CacheHit (242μs)
      • Illuminate\Cache\Events\CacheHit (320μs)
      • Illuminate\Cache\Events\CacheHit (231μs)
      • Illuminate\Cache\Events\CacheHit (379μs)
      • Illuminate\Cache\Events\CacheHit (224μs)
      • Illuminate\Cache\Events\CacheHit (158μs)
      • Illuminate\Cache\Events\CacheHit (288μs)
      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (200μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (192μs)
      • Illuminate\Cache\Events\CacheHit (172μs)
      • Illuminate\Cache\Events\CacheHit (190μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (199μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • creating: site.blocks.subject-homework (1.14ms)
      • composing: site.blocks.subject-homework (26μs)
      • eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (172μs)
      • eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (116μs)
      • Illuminate\Database\Events\StatementPrepared (6.26ms)
      • Illuminate\Database\Events\QueryExecuted (1.03ms)
      • creating: components.homework-blocks (185μs)
      • composing: components.homework-blocks (119μs)
      • creating: site.blocks.reviews (324μs)
      • composing: site.blocks.reviews (22μs)
      • creating: site.blocks.submit-homework (152μs)
      • composing: site.blocks.submit-homework (19μs)
      • creating: site.blocks.faq (109μs)
      • composing: site.blocks.faq (17μs)
      • eloquent.booting: App\Models\Twill\TwillFaq (199μs)
      • eloquent.booted: App\Models\Twill\TwillFaq (169μs)
      • eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (231μs)
      • eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (70μs)
      • Illuminate\Database\Events\StatementPrepared (1.41ms)
      • Illuminate\Database\Events\QueryExecuted (961μs)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (136μs)
      • Illuminate\Database\Events\StatementPrepared (1.06ms)
      • Illuminate\Database\Events\QueryExecuted (854μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (96μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (22μs)
      • creating: components.faq-item (152μs)
      • composing: components.faq-item (102μs)
      • Illuminate\Database\Events\StatementPrepared (4.52ms)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (109μs)
      • Illuminate\Database\Events\StatementPrepared (644μs)
      • Illuminate\Database\Events\QueryExecuted (921μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (78μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (21μs)
      • creating: components.faq-item (87μs)
      • composing: components.faq-item (47μs)
      • Illuminate\Database\Events\StatementPrepared (2.7ms)
      • Illuminate\Database\Events\QueryExecuted (818μs)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (73μs)
      • Illuminate\Database\Events\StatementPrepared (846μs)
      • Illuminate\Database\Events\QueryExecuted (807μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (51μs)
      • creating: components.faq-item (60μs)
      • composing: components.faq-item (37μs)
      • Illuminate\Database\Events\StatementPrepared (1.04ms)
      • Illuminate\Database\Events\QueryExecuted (1.01ms)
      • eloquent.retrieved: App\Models\Twill\TwillFaq (73μs)
      • Illuminate\Database\Events\StatementPrepared (1.06ms)
      • Illuminate\Database\Events\QueryExecuted (739μs)
      • eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (51μs)
      • creating: components.faq-item (58μs)
      • composing: components.faq-item (37μs)
      • creating: site.blocks.text-with-image (383μs)
      • composing: site.blocks.text-with-image (17μs)
      • creating: site.blocks.work-with-tutors (186μs)
      • composing: site.blocks.work-with-tutors (13μs)
      • creating: site.layouts.app (232μs)
      • composing: site.layouts.app (20μs)
      • creating: components.canonical (498μs)
      • composing: components.canonical (100μs)
      • creating: components.open-graph (273μs)
      • composing: components.open-graph (80μs)
      • creating: site.headers.header (264μs)
      • composing: site.headers.header (76μs)
      • Illuminate\Cache\Events\CacheHit (1.85ms)
      • creating: components.footer (73μs)
      • composing: components.footer (89μs)
      • Illuminate\Cache\Events\CacheHit (737μs)
      • Illuminate\Cache\Events\CacheHit (361μs)
      • Illuminate\Cache\Events\CacheHit (300μs)
      • Illuminate\Cache\Events\CacheHit (204μs)
      • Illuminate\Cache\Events\CacheHit (205μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (266μs)
      • Illuminate\Cache\Events\CacheHit (259μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (237μs)
      • Illuminate\Cache\Events\CacheHit (225μs)
      • Illuminate\Cache\Events\CacheHit (335μs)
      • Illuminate\Cache\Events\CacheHit (218μs)
      • creating: components.forms.contact-us (269μs)
      • composing: components.forms.contact-us (182μs)
      • creating: components.forms.get-started (146μs)
      • composing: components.forms.get-started (79μs)
      • creating: components.forms.free-tool-download (99μs)
      • composing: components.forms.free-tool-download (62μs)
      • creating: components.forms.claim-free-worksheet (98μs)
      • composing: components.forms.claim-free-worksheet (62μs)
      • creating: components.forms.tutor-subscription-waitlist (98μs)
      • composing: components.forms.tutor-subscription-waitlist (61μs)
      • creating: components.forms.tutor-subscription-join (97μs)
      • composing: components.forms.tutor-subscription-join (64μs)
      • creating: components.forms.tutor-support (99μs)
      • composing: components.forms.tutor-support (62μs)
      • 630 x Illuminate\Cache\Events\CacheHit (24.91%)
        343ms
        28 x Illuminate\Database\Events\QueryExecuted (7.88%)
        108ms
        28 x Illuminate\Database\Events\StatementPrepared (7.56%)
        104ms
        8 x Illuminate\Cache\Events\KeyWritten (2.02%)
        27.84ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.92%)
        12.68ms
        1 x Illuminate\Routing\Events\RouteMatched (0.8%)
        10.95ms
        6 x creating: components.tutors-card (0.78%)
        10.78ms
        8 x Illuminate\Cache\Events\CacheMissed (0.65%)
        9.01ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.57%)
        7.87ms
        122 x eloquent.retrieved: App\Models\Subject (0.28%)
        3.81ms
        1 x Illuminate\Routing\Events\Routing (0.26%)
        3.60ms
        2 x Illuminate\Database\Events\ConnectionEstablished (0.13%)
        1.75ms
        1 x creating: site.blocks.subject-homework (0.08%)
        1.14ms
        6 x composing: components.tutors-card (0.05%)
        624μs
        1 x creating: components.canonical (0.04%)
        498μs
        1 x eloquent.booting: App\Models\User\TutorAttributes\TutorDegree (0.03%)
        457μs
        4 x eloquent.retrieved: App\Models\Twill\TwillFaq (0.03%)
        391μs
        1 x creating: site.blocks.text-with-image (0.03%)
        383μs
        1 x creating: site.blocks.how-it-works (0.03%)
        375μs
        4 x creating: components.faq-item (0.03%)
        357μs
        1 x eloquent.booting: App\Models\User\Tutor (0.02%)
        332μs
        1 x creating: site.blocks.reviews (0.02%)
        324μs
        6 x eloquent.retrieved: App\Models\Twill\Slugs\TwillFaqSlug (0.02%)
        319μs
        6 x eloquent.retrieved: App\Models\User\Tutor (0.02%)
        311μs
        1 x creating: components.breadcrumbs (0.02%)
        300μs
        1 x creating: components.open-graph (0.02%)
        273μs
        1 x creating: components.forms.contact-us (0.02%)
        269μs
        1 x creating: site.headers.header (0.02%)
        264μs
        1 x creating: site.layouts.app (0.02%)
        232μs
        1 x eloquent.booting: App\Models\Twill\Slugs\TwillFaqSlug (0.02%)
        231μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        228μs
        4 x composing: components.faq-item (0.02%)
        223μs
        1 x creating: components.tutors-cards (0.02%)
        217μs
        1 x eloquent.booted: App\Models\User\Tutor (0.02%)
        207μs
        1 x eloquent.booting: App\Models\Twill\TwillFaq (0.01%)
        199μs
        1 x creating: site.blocks.work-with-tutors (0.01%)
        186μs
        1 x creating: components.homework-blocks (0.01%)
        185μs
        1 x composing: components.forms.contact-us (0.01%)
        182μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.01%)
        172μs
        1 x eloquent.booted: App\Models\Twill\TwillFaq (0.01%)
        169μs
        1 x eloquent.booting: App\Models\Meta (0.01%)
        167μs
        1 x creating: site.blocks.subject-tutors (0.01%)
        154μs
        1 x creating: subjects.show (0.01%)
        153μs
        1 x creating: site.blocks.submit-homework (0.01%)
        152μs
        1 x creating: components.forms.get-started (0.01%)
        146μs
        1 x composing: components.breadcrumbs (0.01%)
        141μs
        1 x composing: components.tutors-cards (0.01%)
        121μs
        1 x eloquent.booted: App\Models\User\TutorAttributes\TutorDegree (0.01%)
        121μs
        1 x composing: components.homework-blocks (0.01%)
        119μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.01%)
        116μs
        1 x composing: subjects.show (0.01%)
        116μs
        1 x eloquent.retrieved: App\Models\Meta (0.01%)
        113μs
        1 x creating: site.blocks.faq (0.01%)
        109μs
        1 x composing: components.canonical (0.01%)
        100μs
        1 x creating: components.forms.tutor-support (0.01%)
        99μs
        1 x creating: components.forms.free-tool-download (0.01%)
        99μs
        1 x creating: components.forms.claim-free-worksheet (0.01%)
        98μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.01%)
        98μs
        1 x creating: components.forms.tutor-subscription-join (0.01%)
        97μs
        1 x composing: components.footer (0.01%)
        89μs
        1 x eloquent.booting: App\Models\SubjectCat (0.01%)
        83μs
        1 x composing: components.open-graph (0.01%)
        80μs
        1 x composing: components.forms.get-started (0.01%)
        79μs
        1 x composing: site.headers.header (0.01%)
        76μs
        1 x creating: components.footer (0.01%)
        73μs
        1 x eloquent.booted: App\Models\Twill\Slugs\TwillFaqSlug (0.01%)
        70μs
        1 x eloquent.booted: App\Models\Subject (0%)
        64μs
        1 x composing: components.forms.tutor-subscription-join (0%)
        64μs
        1 x composing: components.forms.free-tool-download (0%)
        62μs
        1 x composing: components.forms.claim-free-worksheet (0%)
        62μs
        1 x composing: components.forms.tutor-support (0%)
        62μs
        1 x composing: components.forms.tutor-subscription-waitlist (0%)
        61μs
        1 x eloquent.booted: App\Models\SubjectCat (0%)
        58μs
        1 x eloquent.booted: App\Models\Meta (0%)
        56μs
        1 x composing: site.blocks.subject-homework (0%)
        26μs
        1 x composing: site.blocks.how-it-works (0%)
        23μs
        1 x composing: site.blocks.reviews (0%)
        22μs
        1 x composing: site.layouts.app (0%)
        20μs
        1 x composing: site.blocks.subject-tutors (0%)
        19μs
        1 x composing: site.blocks.submit-homework (0%)
        19μs
        1 x composing: site.blocks.faq (0%)
        17μs
        1 x composing: site.blocks.text-with-image (0%)
        17μs
        1 x composing: site.blocks.work-with-tutors (0%)
        13μs
      34 templates were rendered
      • 1x subjects.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.blocks.how-it-workshow-it-works.blade.phpblade
      • 1x site.blocks.subject-tutorssubject-tutors.blade.phpblade
      • 1x components.tutors-cardstutors-cards.blade.phpblade
      • 6x components.tutors-cardtutors-card.blade.phpblade
      • 1x site.blocks.subject-homeworksubject-homework.blade.phpblade
      • 1x components.homework-blockshomework-blocks.blade.phpblade
      • 1x site.blocks.reviewsreviews.blade.phpblade
      • 1x site.blocks.submit-homeworksubmit-homework.blade.phpblade
      • 1x site.blocks.faqfaq.blade.phpblade
      • 4x components.faq-itemfaq-item.blade.phpblade
      • 1x site.blocks.text-with-imagetext-with-image.blade.phpblade
      • 1x site.blocks.work-with-tutorswork-with-tutors.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET subjects/{categoryUri}/{subjectUri?}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\SubjectController@show
      namespace
      where
      as
      subjects.show
      file
      app/Http/Controllers/SubjectController.php:43-96
      28 statements were executed164ms
      • Connection Establishedtwenty4_siteSubjectRepository.php#123
        Backtrace
        • 13. app/Repositories/SubjectRepository.php:123
        • 14. app/Http/Controllers/SubjectController.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `subjects` where `urlFriendlyTitle` = 'Ergodic-Theory' limit 1
        14.21mstwenty4_siteSubjectRepository.php#123
        Bindings
        • 0: Ergodic-Theory
        Backtrace
        • 15. app/Repositories/SubjectRepository.php:123
        • 16. app/Http/Controllers/SubjectController.php:54
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `subject_cats` where `subject_cats`.`id` in (1)
        16.47mstwenty4_siteSubjectRepository.php#123
        Backtrace
        • 20. app/Repositories/SubjectRepository.php:123
        • 21. app/Http/Controllers/SubjectController.php:54
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `meta` where `meta`.`id` = 3 limit 1
        7.19mstwenty4_siteMetaService.php#118
        Bindings
        • 0: 3
        Backtrace
        • 19. app/Services/MetaService.php:118
        • 20. app/Services/MetaService.php:108
        • 21. app/Services/MetaService.php:81
        • 22. app/Http/Controllers/SubjectController.php:89
        • 23. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • Connection Establishedtwenty4_siteTutorRepository.php#40
        Backtrace
        • 13. app/Repositories/TutorRepository.php:40
        • 14. app/View/Components/TutorsCards.php:28
        • 15. app/View/Components/TutorsCards.php:22
        • 17. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
      • select count(*) as aggregate from `users` where (`subjectsQualified` like '%|126|%' or `DSF_subjectsQualified` like '%|126|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor'
        18.15mstwenty4_siteTutorsCards.php#35
        Bindings
        • 0: %|126|%
        • 1: %|126|%
        • 2: 1
        • 3: 0
        • 4: 
        • 5: 1
        • 6: 0
        • 7: 0
        • 8: 
        • 9: tutor
        Backtrace
        • 15. app/View/Components/TutorsCards.php:35
        • 16. app/View/Components/TutorsCards.php:22
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
        • 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933
      • select * from `users` where (`subjectsQualified` like '%|126|%' or `DSF_subjectsQualified` like '%|126|%' or `allsubjects` = 1) and `disable_profile` = 0 and `picture` != '' and `solutionrequestQualified` = 1 and `is_suspended` = 0 and `is_deactivated` = 0 and `status` != '' and `status` = 'tutor' order by `completed_requests` desc limit 6 offset 0
        11.5mstwenty4_siteTutorsCards.php#35
        Bindings
        • 0: %|126|%
        • 1: %|126|%
        • 2: 1
        • 3: 0
        • 4: 
        • 5: 1
        • 6: 0
        • 7: 0
        • 8: 
        • 9: tutor
        Backtrace
        • 15. app/View/Components/TutorsCards.php:35
        • 16. app/View/Components/TutorsCards.php:22
        • 18. vendor/laravel/framework/src/Illuminate/Container/Container.php:929
        • 19. vendor/laravel/framework/src/Illuminate/Container/Container.php:770
        • 20. vendor/laravel/framework/src/Illuminate/Foundation/Application.php:933
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 2821 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        1.06mstwenty4_siteTutor.php#361
        Bindings
        • 0: 2821
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 76351 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        1.38mstwenty4_siteTutor.php#361
        Bindings
        • 0: 76351
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        5.09mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 42 limit 1
        19.83mstwenty4_siteSubject.php#100
        Bindings
        • 0: 42
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 96652 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        4.15mstwenty4_siteTutor.php#361
        Bindings
        • 0: 96652
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (240, 119, 245, 134, 2, 160, 133, 1, 6, 127, 123, 229, 70, 10, 122, 257, 220, 126, 124, 65, 7, 3, 349, 9, 66, 60, 125, 68, 47, 73, 348, 41, 8, 347, 299, 121, 4, 15)
        7.84mstwenty4_siteTutor.php#214
        Bindings
        • 0: 240
        • 1: 119
        • 2: 245
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        • 4: 2
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        • 7: 1
        • 8: 6
        • 9: 127
        • 10: 123
        • 11: 229
        • 12: 70
        • 13: 10
        • 14: 122
        • 15: 257
        • 16: 220
        • 17: 126
        • 18: 124
        • 19: 65
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        • 21: 3
        • 22: 349
        • 23: 9
        • 24: 66
        • 25: 60
        • 26: 125
        • 27: 68
        • 28: 47
        • 29: 73
        • 30: 348
        • 31: 41
        • 32: 8
        • 33: 347
        • 34: 299
        • 35: 121
        • 36: 4
        • 37: 15
        Backtrace
        • 14. app/Models/User/Tutor.php:214
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Models/User/Tutor.php:216
        • 24. app/Models/User/Tutor.php:267
      • select * from `subject_cats` where `subject_cats`.`id` in (1, 3, 31)
        1.5mstwenty4_siteTutor.php#214
        Backtrace
        • 19. app/Models/User/Tutor.php:214
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Models/User/Tutor.php:216
        • 29. app/Models/User/Tutor.php:267
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 174502 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        7.41mstwenty4_siteTutor.php#361
        Bindings
        • 0: 174502
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (200, 142, 18, 50, 15, 130, 144, 354, 72, 259, 108, 143, 115, 52, 240, 119, 245, 34, 134, 2, 160, 133, 1, 6, 127, 123, 229, 70, 10, 122, 257, 220, 126, 124, 65, 7, 3, 349, 9, 396, 66, 125, 68, 47, 73, 348, 41, 8, 71, 347, 67, 48, 299, 121, 4, 394)
        10.4mstwenty4_siteTutor.php#214
        Bindings
        • 0: 200
        • 1: 142
        • 2: 18
        • 3: 50
        • 4: 15
        • 5: 130
        • 6: 144
        • 7: 354
        • 8: 72
        • 9: 259
        • 10: 108
        • 11: 143
        • 12: 115
        • 13: 52
        • 14: 240
        • 15: 119
        • 16: 245
        • 17: 34
        • 18: 134
        • 19: 2
        • 20: 160
        • 21: 133
        • 22: 1
        • 23: 6
        • 24: 127
        • 25: 123
        • 26: 229
        • 27: 70
        • 28: 10
        • 29: 122
        • 30: 257
        • 31: 220
        • 32: 126
        • 33: 124
        • 34: 65
        • 35: 7
        • 36: 3
        • 37: 349
        • 38: 9
        • 39: 396
        • 40: 66
        • 41: 125
        • 42: 68
        • 43: 47
        • 44: 73
        • 45: 348
        • 46: 41
        • 47: 8
        • 48: 71
        • 49: 347
        • 50: 67
        • 51: 48
        • 52: 299
        • 53: 121
        • 54: 4
        • 55: 394
        Backtrace
        • 14. app/Models/User/Tutor.php:214
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Models/User/Tutor.php:216
        • 24. app/Models/User/Tutor.php:267
      • select * from `subject_cats` where `subject_cats`.`id` in (1, 3, 10, 31)
        2.38mstwenty4_siteTutor.php#214
        Backtrace
        • 19. app/Models/User/Tutor.php:214
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Models/User/Tutor.php:216
        • 29. app/Models/User/Tutor.php:267
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 77733 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        1.28mstwenty4_siteTutor.php#361
        Bindings
        • 0: 77733
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select `subjects`.*, `subject_cats`.`title` as `category_title`, `subject_cats`.`id` as `category_id` from `subjects` inner join `subject_cats` on `subject_cats`.`id` = `subjects`.`catID` where `subjects`.`id` in (119, 34, 160, 6, 123, 122, 257, 220, 126, 124, 3, 9, 66, 125, 68, 8, 347, 67, 121, 129, 512, 103, 142, 15, 128, 139, 143)
        12.5mstwenty4_siteTutor.php#214
        Bindings
        • 0: 119
        • 1: 34
        • 2: 160
        • 3: 6
        • 4: 123
        • 5: 122
        • 6: 257
        • 7: 220
        • 8: 126
        • 9: 124
        • 10: 3
        • 11: 9
        • 12: 66
        • 13: 125
        • 14: 68
        • 15: 8
        • 16: 347
        • 17: 67
        • 18: 121
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        • 21: 103
        • 22: 142
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        • 24: 128
        • 25: 139
        • 26: 143
        Backtrace
        • 14. app/Models/User/Tutor.php:214
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Models/User/Tutor.php:216
        • 24. app/Models/User/Tutor.php:267
      • select * from `subject_cats` where `subject_cats`.`id` in (1, 3)
        1.12mstwenty4_siteTutor.php#214
        Backtrace
        • 19. app/Models/User/Tutor.php:214
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Models/User/Tutor.php:216
        • 29. app/Models/User/Tutor.php:267
      • select * from `tutor_degrees` where `tutor_degrees`.`tutor_id` = 95841 and `tutor_degrees`.`tutor_id` is not null order by `year` desc limit 1
        2.8mstwenty4_siteTutor.php#361
        Bindings
        • 0: 95841
        Backtrace
        • 18. app/Models/User/Tutor.php:361
        • 19. view::components.tutors-card:11
        • 21. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
      • select count(*) as aggregate from `solutionslibrary` where exists (select * from `subjects` where `solutionslibrary`.`subject` = `subjects`.`id`) and `subject` = 126 and `status` = 'published' and `price` > 0
        6.05mstwenty4_siteHomeworkBlocks.php#27
        Bindings
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        Backtrace
        • 15. app/View/Components/HomeworkBlocks.php:27
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.subject-homework:4
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
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        1.45mstwenty4_siteFaqItem.php#15
        Bindings
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        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:7
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (1) and `twill_faq_slugs`.`deleted_at` is null
        1.29mstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:7
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'can-you-help-me-with-my-examquiztest' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        4.15mstwenty4_siteFaqItem.php#15
        Bindings
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        • 1: 1
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        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:24
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (2) and `twill_faq_slugs`.`deleted_at` is null
        830μstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:24
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'how-much-will-it-cost' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        1mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: how-much-will-it-cost
        • 1: 1
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        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:41
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (3) and `twill_faq_slugs`.`deleted_at` is null
        980μstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:41
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faqs` where exists (select * from `twill_faq_slugs` where `twill_faqs`.`id` = `twill_faq_slugs`.`twill_faq_id` and `slug` = 'what-kind-of-payments-do-you-accept' and `active` = 1 and `locale` = 'en' and `twill_faq_slugs`.`deleted_at` is null) and `twill_faqs`.`deleted_at` is null limit 1
        1.07mstwenty4_siteFaqItem.php#15
        Bindings
        • 0: what-kind-of-payments-do-you-accept
        • 1: 1
        • 2: en
        Backtrace
        • 15. app/View/Components/FaqItem.php:15
        • 16. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 17. view::site.blocks.faq:58
        • 19. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 20. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • select * from `twill_faq_slugs` where `twill_faq_slugs`.`twill_faq_id` in (4) and `twill_faq_slugs`.`deleted_at` is null
        900μstwenty4_siteFaqItem.php#15
        Backtrace
        • 20. app/View/Components/FaqItem.php:15
        • 21. vendor/laravel/framework/src/Illuminate/View/Component.php:102
        • 22. view::site.blocks.faq:58
        • 24. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 25. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      App\Models\Subject
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