Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (mathematical analysis). It has no generally accepted definition.
No discussions were found.
Debug Trace
| Info | Could not find file 'oauth2.css' in folder 'oauth2'. |
| Notice |
Trying to access array offset on value of type bool
#0 /home/xtreabfi/kuppiya/cache/Smarty/compile/vanilla^8d148c5e1b13e8d27851611d20a380b18401257f_0.file.default.master.tpl.php(45): gdn_ErrorHandler(8, 'Trying to acces...', '/home/xtreabfi/...', 45, Array)
#1 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_resource_base.php(123): content_6594354daaee31_19788427(Object(Smarty_Internal_Template))
#2 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_compiled.php(114): Smarty_Template_Resource_Base->getRenderedTemplateCode(Object(Smarty_Internal_Template))
#3 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_template.php(216): Smarty_Template_Compiled->render(Object(Smarty_Internal_Template))
#4 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(232): Smarty_Internal_Template->render(false, 1)
#5 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(134): Smarty_Internal_TemplateBase->_execute(Object(Smarty_Internal_Template), NULL, 'vanilla', NULL, 1)
#6 /home/xtreabfi/kuppiya/library/core/class.smarty.php(146): Smarty_Internal_TemplateBase->display('/home/xtreabfi/...', NULL, 'vanilla')
#7 /home/xtreabfi/kuppiya/library/core/class.controller.php(2232): Gdn_Smarty->render('/home/xtreabfi/...', Object(CategoriesController))
#8 /home/xtreabfi/kuppiya/library/core/class.controller.php(1595): Gdn_Controller->renderMaster()
#9 /home/xtreabfi/kuppiya/library/core/class.pluggable.php(217): Gdn_Controller->xRender()
#10 /home/xtreabfi/kuppiya/applications/vanilla/controllers/class.categoriescontroller.php(537): Gdn_Pluggable->__call('render', Array)
#11 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(933): CategoriesController->index('mathematics', 1)
#12 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(335): Gdn_Dispatcher->dispatchController(Object(Gdn_Request), Array)
#13 /home/xtreabfi/kuppiya/index.php(29): Gdn_Dispatcher->dispatch()
#14 {main} |
| Notice |
Trying to access array offset on value of type bool
#0 /home/xtreabfi/kuppiya/cache/Smarty/compile/vanilla^8d148c5e1b13e8d27851611d20a380b18401257f_0.file.default.master.tpl.php(125): gdn_ErrorHandler(8, 'Trying to acces...', '/home/xtreabfi/...', 125, Array)
#1 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_resource_base.php(123): content_6594354daaee31_19788427(Object(Smarty_Internal_Template))
#2 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_compiled.php(114): Smarty_Template_Resource_Base->getRenderedTemplateCode(Object(Smarty_Internal_Template))
#3 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_template.php(216): Smarty_Template_Compiled->render(Object(Smarty_Internal_Template))
#4 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(232): Smarty_Internal_Template->render(false, 1)
#5 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(134): Smarty_Internal_TemplateBase->_execute(Object(Smarty_Internal_Template), NULL, 'vanilla', NULL, 1)
#6 /home/xtreabfi/kuppiya/library/core/class.smarty.php(146): Smarty_Internal_TemplateBase->display('/home/xtreabfi/...', NULL, 'vanilla')
#7 /home/xtreabfi/kuppiya/library/core/class.controller.php(2232): Gdn_Smarty->render('/home/xtreabfi/...', Object(CategoriesController))
#8 /home/xtreabfi/kuppiya/library/core/class.controller.php(1595): Gdn_Controller->renderMaster()
#9 /home/xtreabfi/kuppiya/library/core/class.pluggable.php(217): Gdn_Controller->xRender()
#10 /home/xtreabfi/kuppiya/applications/vanilla/controllers/class.categoriescontroller.php(537): Gdn_Pluggable->__call('render', Array)
#11 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(933): CategoriesController->index('mathematics', 1)
#12 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(335): Gdn_Dispatcher->dispatchController(Object(Gdn_Request), Array)
#13 /home/xtreabfi/kuppiya/index.php(29): Gdn_Dispatcher->dispatch()
#14 {main} |
| Notice |
Trying to access array offset on value of type bool
#0 /home/xtreabfi/kuppiya/cache/Smarty/compile/vanilla^8d148c5e1b13e8d27851611d20a380b18401257f_0.file.default.master.tpl.php(219): gdn_ErrorHandler(8, 'Trying to acces...', '/home/xtreabfi/...', 219, Array)
#1 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_resource_base.php(123): content_6594354daaee31_19788427(Object(Smarty_Internal_Template))
#2 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_compiled.php(114): Smarty_Template_Resource_Base->getRenderedTemplateCode(Object(Smarty_Internal_Template))
#3 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_template.php(216): Smarty_Template_Compiled->render(Object(Smarty_Internal_Template))
#4 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(232): Smarty_Internal_Template->render(false, 1)
#5 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(134): Smarty_Internal_TemplateBase->_execute(Object(Smarty_Internal_Template), NULL, 'vanilla', NULL, 1)
#6 /home/xtreabfi/kuppiya/library/core/class.smarty.php(146): Smarty_Internal_TemplateBase->display('/home/xtreabfi/...', NULL, 'vanilla')
#7 /home/xtreabfi/kuppiya/library/core/class.controller.php(2232): Gdn_Smarty->render('/home/xtreabfi/...', Object(CategoriesController))
#8 /home/xtreabfi/kuppiya/library/core/class.controller.php(1595): Gdn_Controller->renderMaster()
#9 /home/xtreabfi/kuppiya/library/core/class.pluggable.php(217): Gdn_Controller->xRender()
#10 /home/xtreabfi/kuppiya/applications/vanilla/controllers/class.categoriescontroller.php(537): Gdn_Pluggable->__call('render', Array)
#11 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(933): CategoriesController->index('mathematics', 1)
#12 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(335): Gdn_Dispatcher->dispatchController(Object(Gdn_Request), Array)
#13 /home/xtreabfi/kuppiya/index.php(29): Gdn_Dispatcher->dispatch()
#14 {main} |
| Notice |
Trying to access array offset on value of type bool
#0 /home/xtreabfi/kuppiya/cache/Smarty/compile/vanilla^8d148c5e1b13e8d27851611d20a380b18401257f_0.file.default.master.tpl.php(235): gdn_ErrorHandler(8, 'Trying to acces...', '/home/xtreabfi/...', 235, Array)
#1 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_resource_base.php(123): content_6594354daaee31_19788427(Object(Smarty_Internal_Template))
#2 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_compiled.php(114): Smarty_Template_Resource_Base->getRenderedTemplateCode(Object(Smarty_Internal_Template))
#3 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_template.php(216): Smarty_Template_Compiled->render(Object(Smarty_Internal_Template))
#4 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(232): Smarty_Internal_Template->render(false, 1)
#5 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(134): Smarty_Internal_TemplateBase->_execute(Object(Smarty_Internal_Template), NULL, 'vanilla', NULL, 1)
#6 /home/xtreabfi/kuppiya/library/core/class.smarty.php(146): Smarty_Internal_TemplateBase->display('/home/xtreabfi/...', NULL, 'vanilla')
#7 /home/xtreabfi/kuppiya/library/core/class.controller.php(2232): Gdn_Smarty->render('/home/xtreabfi/...', Object(CategoriesController))
#8 /home/xtreabfi/kuppiya/library/core/class.controller.php(1595): Gdn_Controller->renderMaster()
#9 /home/xtreabfi/kuppiya/library/core/class.pluggable.php(217): Gdn_Controller->xRender()
#10 /home/xtreabfi/kuppiya/applications/vanilla/controllers/class.categoriescontroller.php(537): Gdn_Pluggable->__call('render', Array)
#11 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(933): CategoriesController->index('mathematics', 1)
#12 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(335): Gdn_Dispatcher->dispatchController(Object(Gdn_Request), Array)
#13 /home/xtreabfi/kuppiya/index.php(29): Gdn_Dispatcher->dispatch()
#14 {main} |
| Notice |
Undefined index: internal
#0 /home/xtreabfi/kuppiya/library/core/class.router.php(70): gdn_ErrorHandler(8, 'Undefined index...', '/home/xtreabfi/...', 70, Array)
#1 /home/xtreabfi/kuppiya/library/core/class.theme.php(92): Gdn_Router->getRoute('DefaultControll...')
#2 /home/xtreabfi/kuppiya/library/SmartyPlugins/function.breadcrumbs.php(24): Gdn_Theme::breadcrumbs(Array, true, Array)
#3 /home/xtreabfi/kuppiya/cache/Smarty/compile/vanilla^8d148c5e1b13e8d27851611d20a380b18401257f_0.file.default.master.tpl.php(332): smarty_function_breadcrumbs(Array, Object(Smarty_Internal_Template))
#4 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_resource_base.php(123): content_6594354daaee31_19788427(Object(Smarty_Internal_Template))
#5 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_template_compiled.php(114): Smarty_Template_Resource_Base->getRenderedTemplateCode(Object(Smarty_Internal_Template))
#6 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_template.php(216): Smarty_Template_Compiled->render(Object(Smarty_Internal_Template))
#7 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(232): Smarty_Internal_Template->render(false, 1)
#8 /home/xtreabfi/kuppiya/vendor/smarty/smarty/libs/sysplugins/smarty_internal_templatebase.php(134): Smarty_Internal_TemplateBase->_execute(Object(Smarty_Internal_Template), NULL, 'vanilla', NULL, 1)
#9 /home/xtreabfi/kuppiya/library/core/class.smarty.php(146): Smarty_Internal_TemplateBase->display('/home/xtreabfi/...', NULL, 'vanilla')
#10 /home/xtreabfi/kuppiya/library/core/class.controller.php(2232): Gdn_Smarty->render('/home/xtreabfi/...', Object(CategoriesController))
#11 /home/xtreabfi/kuppiya/library/core/class.controller.php(1595): Gdn_Controller->renderMaster()
#12 /home/xtreabfi/kuppiya/library/core/class.pluggable.php(217): Gdn_Controller->xRender()
#13 /home/xtreabfi/kuppiya/applications/vanilla/controllers/class.categoriescontroller.php(537): Gdn_Pluggable->__call('render', Array)
#14 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(933): CategoriesController->index('mathematics', 1)
#15 /home/xtreabfi/kuppiya/library/core/class.dispatcher.php(335): Gdn_Dispatcher->dispatchController(Object(Gdn_Request), Array)
#16 /home/xtreabfi/kuppiya/index.php(29): Gdn_Dispatcher->dispatch()
#17 {main} |