• 根据孩子未来的实际需要,在学科同步辅导、竞赛培优冲奖
  • G5牛剑笔面、国际择校与研究生考试辅导等方面综合规划
  • 为孩子进行同步辅导和培优,帮助孩子在短时间内提升硬实力

400-888-4846

昆明犀牛国际教育HiMCM数学建模竞赛培训:从知识体系到实战技巧的全维度提升方案

昆明犀牛国际教育HiMCM数学建模竞赛培训:从知识体系到实战技巧的全维度提升方案

授课机构: 昆明犀牛国际教育

上课地点: 校区地址

成交/评价:

联系电话: 400-888-4846

昆明犀牛国际教育HiMCM数学建模竞赛培训:从知识体系到实战技巧的全维度提升方案课程详情

HiMCM数学建模竞赛培训:如何通过系统学习突破国际竞赛瓶颈?

HiMCM竞赛:国际认可的中学生数学能力试金石

对于有意向在理工科领域发展的高中生而言,HiMCM(High School Mathematical Contest in Modeling)美国高中生数学建模竞赛是一块重要的能力证明拼图。这项由美国数学及其应用联合会(COMAP)主办的赛事,自1999年首届举办以来,已发展为全球三大数学建模竞赛之一,2023年参赛规模覆盖40余个国家和地区的上万名学生。其独特之处在于,竞赛不仅考察数学知识的应用能力,更强调团队协作、问题分析及学术写作等综合素养,因此参赛成绩常被国内外高校作为本科生选拔的重要参考依据。

从竞赛形式看,HiMCM采用线上团队合作模式,要求2-4人组队完成建模论文。时间固定在每年11月,持续约4天。奖项设置上,仅有1%的队伍能获得特等奖,7%获特等奖提名奖,26%获一等奖,34%获二等奖,所有完成论文的参赛者均可获参与奖。这种阶梯式奖励机制,既了竞赛的高含金量,也为不同水平的学生提供了展示平台。

昆明犀牛国际教育的多元课程体系:适配不同学习需求

针对HiMCM竞赛的复杂性和个性化需求,昆明犀牛国际教育设计了灵活的课程模式,包括1对1、1对3、1对6及线上线下融合教学。这种分层设置充分考虑了学生的基础差异——数学基础薄弱或时间紧张的学员可选择1对1私教,获得定制化指导;希望通过小组讨论激发思维的学生则适合1对3或1对6班型,在团队协作中提前适应竞赛模式。

课程目标明确指向竞赛核心能力提升:一方面系统梳理数学建模所需的知识点,涵盖模型构建、数据处理、软件操作等关键环节;另一方面通过大量真题演练,帮助学员熟悉竞赛题型、把握难点重点,最终实现高分冲刺。无论是初次接触建模的新手,还是有过参赛经验想突破瓶颈的学生,都能在这里找到匹配的学习路径。

20大核心模块:从理论到实战的全流程覆盖

昆明犀牛国际教育的HiMCM培训课程大纲,围绕“知识-技能-应用”三维目标设计,包含20个细分模块,全面覆盖竞赛所需的核心能力:

  1. 基础模型与数学工具:从常见模型的方程求解入手,逐步深入热传导模型计算、坐标转换、转移状态矩阵等基础内容,夯实建模数学基础。
  2. 随机过程与概率统计:讲解随机微分方程、离散变量处理、普通布朗运动及伊藤过程,结合泊松分布、帕累托分布等概率模型,提升复杂问题建模能力。
  3. 数值方法与软件操作:系统教授时域有限差分、网格法、有限元等数值计算方法,同时强化统计软件操作(如SPSS、R语言)及常用回归分析技巧,确保学员能熟练运用工具解决实际问题。
  4. 高级算法与模型拓展:涵盖蒙特卡洛、Bagging、AdaBoost等集成学习方法,梯度算法、逻辑回归及人工神经网络等机器学习模型,帮助学员应对前沿竞赛选题。
  5. 实战指导与学术规范:针对生物工程、计量经济等具体领域选题提供个性化指导,包括文献查阅技巧、数据处理规范、图表展示科学方法,以及摘要撰写、研究总结的学术表达训练,确保论文符合竞赛评审标准。

值得关注的是,课程特别设置了“选题针对性指导”模块,教师会根据学员兴趣方向(如机械工程、流体力学等)提供定制化辅导,避免“一刀切”教学。同时,通过模拟竞赛流程,让学员在限时团队协作中积累实战经验,缩短理论到应用的转化周期。

为什么选择昆明犀牛国际教育?

区别于常规竞赛培训,昆明犀牛国际教育的优势体现在三个方面:

师资专业性:授课教师均具备数学建模竞赛指导经验,部分教师曾参与HiMCM评审,熟悉评分细则和常见扣分点,能精准定位学员问题并提供解决方案。

教学体系化:课程不仅包含知识点讲解,更注重思维训练——通过“问题拆解-模型构建-结果验证-论文撰写”的完整流程教学,培养学员从复杂问题中提取数学本质的能力。

服务个性化:针对不同班型设置分层作业和反馈机制,1对1课程提供周报式学习跟踪,1对3/6班型通过小组互评激发学习动力,确保每个学员的学习进度和效果可量化、可提升。

写在最后:HiMCM竞赛的长远价值

参加HiMCM竞赛的意义远不止于获得奖项。通过系统的建模训练,学员将掌握跨学科问题解决能力、数据驱动决策思维及学术写作技巧,这些能力不仅是竞赛制胜的关键,更是未来大学学习和科研工作的核心竞争力。昆明犀牛国际教育的HiMCM培训课程,正是以“提升核心能力”为导向,帮助学生在竞赛中成长,为未来的学术道路奠定坚实基础。

昆明犀牛国际教育

昆明犀牛国际教育
认证 7 年

成立: 2006年

认证 地址认证 教学保障 在线预约 到店体验 售后支持
基本 文件 流程 错误 SQL 调试
  1. 请求信息 : 2026-04-18 03:28:55 HTTP/1.1 GET : http://www.aabrg.com/s/6837/c/94033.html
  2. 运行时间 : 0.047580s [ 吞吐率:21.02req/s ] 内存消耗:389.18kb 文件加载:136
  3. 缓存信息 : 0 reads,0 writes
  1. /data/web/baijiao_branch_collect/public/index.php ( 0.79 KB )
  2. /data/web/baijiao_branch_collect/vendor/autoload.php ( 0.75 KB )
  3. /data/web/baijiao_branch_collect/vendor/composer/autoload_real.php ( 1.63 KB )
  4. /data/web/baijiao_branch_collect/vendor/composer/platform_check.php ( 0.90 KB )
  5. /data/web/baijiao_branch_collect/vendor/composer/ClassLoader.php ( 15.99 KB )
  6. /data/web/baijiao_branch_collect/vendor/composer/autoload_static.php ( 4.26 KB )
  7. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/helper.php ( 8.34 KB )
  8. /data/web/baijiao_branch_collect/vendor/topthink/think-validate/src/helper.php ( 2.19 KB )
  9. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/helper.php ( 1.47 KB )
  10. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
  11. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
  12. /data/web/baijiao_branch_collect/vendor/topthink/think-container/src/Facade.php ( 2.71 KB )
  13. /data/web/baijiao_branch_collect/vendor/symfony/deprecation-contracts/function.php ( 0.99 KB )
  14. /data/web/baijiao_branch_collect/vendor/symfony/polyfill-mbstring/bootstrap.php ( 8.26 KB )
  15. /data/web/baijiao_branch_collect/vendor/symfony/polyfill-mbstring/bootstrap80.php ( 9.78 KB )
  16. /data/web/baijiao_branch_collect/vendor/symfony/var-dumper/Resources/functions/dump.php ( 1.49 KB )
  17. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/App.php ( 15.30 KB )
  18. /data/web/baijiao_branch_collect/vendor/topthink/think-container/src/Container.php ( 15.76 KB )
  19. /data/web/baijiao_branch_collect/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
  20. /data/web/baijiao_branch_collect/app/provider.php ( 0.19 KB )
  21. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Http.php ( 6.04 KB )
  22. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/helper/Str.php ( 7.29 KB )
  23. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Env.php ( 4.68 KB )
  24. /data/web/baijiao_branch_collect/app/common.php ( 10.83 KB )
  25. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/helper.php ( 18.78 KB )
  26. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Config.php ( 5.54 KB )
  27. /data/web/baijiao_branch_collect/config/app.php ( 1.29 KB )
  28. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
  29. /data/web/baijiao_branch_collect/config/cache.php ( 1.22 KB )
  30. /data/web/baijiao_branch_collect/config/config.php ( 0.26 KB )
  31. /data/web/baijiao_branch_collect/config/console.php ( 0.29 KB )
  32. /data/web/baijiao_branch_collect/config/cookie.php ( 0.56 KB )
  33. /data/web/baijiao_branch_collect/config/database.php ( 2.29 KB )
  34. /data/web/baijiao_branch_collect/config/filesystem.php ( 0.63 KB )
  35. /data/web/baijiao_branch_collect/config/lang.php ( 0.81 KB )
  36. /data/web/baijiao_branch_collect/config/log.php ( 1.37 KB )
  37. /data/web/baijiao_branch_collect/config/middleware.php ( 0.19 KB )
  38. /data/web/baijiao_branch_collect/config/route.php ( 1.54 KB )
  39. /data/web/baijiao_branch_collect/config/session.php ( 0.57 KB )
  40. /data/web/baijiao_branch_collect/config/trace.php ( 0.34 KB )
  41. /data/web/baijiao_branch_collect/config/view.php ( 0.81 KB )
  42. /data/web/baijiao_branch_collect/app/event.php ( 0.25 KB )
  43. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Event.php ( 7.67 KB )
  44. /data/web/baijiao_branch_collect/app/service.php ( 0.13 KB )
  45. /data/web/baijiao_branch_collect/app/AppService.php ( 0.26 KB )
  46. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Service.php ( 1.64 KB )
  47. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Lang.php ( 7.35 KB )
  48. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/lang/zh-cn.php ( 13.70 KB )
  49. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/initializer/Error.php ( 3.31 KB )
  50. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
  51. /data/web/baijiao_branch_collect/vendor/services.php ( 0.14 KB )
  52. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
  53. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
  54. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/service/ModelService.php ( 2.04 KB )
  55. /data/web/baijiao_branch_collect/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
  56. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Middleware.php ( 6.72 KB )
  57. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
  58. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/Paginator.php ( 11.86 KB )
  59. /data/web/baijiao_branch_collect/vendor/topthink/think-validate/src/Validate.php ( 63.20 KB )
  60. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/Model.php ( 23.55 KB )
  61. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 21.05 KB )
  62. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/AutoWriteData.php ( 4.20 KB )
  63. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 6.75 KB )
  64. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/DbConnect.php ( 5.16 KB )
  65. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.33 KB )
  66. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 28.30 KB )
  67. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
  68. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
  69. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/contract/Modelable.php ( 0.09 KB )
  70. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Db.php ( 2.88 KB )
  71. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/DbManager.php ( 8.52 KB )
  72. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Log.php ( 6.28 KB )
  73. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Manager.php ( 3.92 KB )
  74. /data/web/baijiao_branch_collect/vendor/psr/log/src/LoggerTrait.php ( 2.69 KB )
  75. /data/web/baijiao_branch_collect/vendor/psr/log/src/LoggerInterface.php ( 2.71 KB )
  76. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Cache.php ( 4.92 KB )
  77. /data/web/baijiao_branch_collect/vendor/psr/simple-cache/src/CacheInterface.php ( 4.71 KB )
  78. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/helper/Arr.php ( 17.45 KB )
  79. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/cache/driver/Redis.php ( 6.94 KB )
  80. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/cache/Driver.php ( 9.03 KB )
  81. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 1.99 KB )
  82. /data/web/baijiao_branch_collect/app/Request.php ( 0.09 KB )
  83. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Request.php ( 55.78 KB )
  84. /data/web/baijiao_branch_collect/app/middleware.php ( 0.26 KB )
  85. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
  86. /data/web/baijiao_branch_collect/vendor/topthink/think-trace/src/TraceDebug.php ( 3.40 KB )
  87. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Route.php ( 23.73 KB )
  88. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/RuleName.php ( 5.75 KB )
  89. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Domain.php ( 2.53 KB )
  90. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/RuleGroup.php ( 22.43 KB )
  91. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Rule.php ( 26.95 KB )
  92. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/RuleItem.php ( 9.78 KB )
  93. /data/web/baijiao_branch_collect/route/app.php ( 3.05 KB )
  94. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Route.php ( 4.70 KB )
  95. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 4.74 KB )
  96. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Dispatch.php ( 10.44 KB )
  97. /data/web/baijiao_branch_collect/app/controller/Index.php ( 33.26 KB )
  98. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Request.php ( 9.20 KB )
  99. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Url.php ( 14.07 KB )
  100. /data/web/baijiao_branch_collect/app/model/IndexModel.php ( 19.95 KB )
  101. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Config.php ( 1.37 KB )
  102. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Cache.php ( 2.06 KB )
  103. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/facade/Db.php ( 0.93 KB )
  104. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 5.73 KB )
  105. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/PDOConnection.php ( 53.74 KB )
  106. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/Connection.php ( 8.39 KB )
  107. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.57 KB )
  108. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 16.58 KB )
  109. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/Builder.php ( 24.07 KB )
  110. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/BaseBuilder.php ( 27.50 KB )
  111. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/Query.php ( 15.97 KB )
  112. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/BaseQuery.php ( 45.13 KB )
  113. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.43 KB )
  114. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
  115. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 20.07 KB )
  116. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.66 KB )
  117. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 7.01 KB )
  118. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 19.37 KB )
  119. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 7.11 KB )
  120. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.63 KB )
  121. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.77 KB )
  122. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/log/driver/File.php ( 5.96 KB )
  123. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
  124. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/log/Channel.php ( 3.89 KB )
  125. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/event/LogRecord.php ( 1.02 KB )
  126. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/Collection.php ( 16.47 KB )
  127. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Response.php ( 8.81 KB )
  128. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/response/View.php ( 3.29 KB )
  129. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Cookie.php ( 6.06 KB )
  130. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/View.php ( 4.39 KB )
  131. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/view/driver/Php.php ( 6.44 KB )
  132. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/contract/TemplateHandlerInterface.php ( 1.60 KB )
  133. /data/web/baijiao_branch_collect/view/index/pc/school_course_details.php ( 6.12 KB )
  134. /data/web/baijiao_branch_collect/view/index/pc/school_top.php ( 5.76 KB )
  135. /data/web/baijiao_branch_collect/view/index/pc/school_bottom.php ( 1.16 KB )
  136. /data/web/baijiao_branch_collect/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000288s ] mysql:host=127.0.0.1;port=3306;dbname=baijiao_branch_collect;charset=utf8
  2. SHOW FULL COLUMNS FROM `fqi_school` [ RunTime:0.000962s ]
  3. SELECT * FROM `fqi_school` WHERE `school_id` = '6837' AND `site_id` = 22 AND `school_status` = 1 LIMIT 1 [ RunTime:0.000266s ]
  4. SHOW FULL COLUMNS FROM `fqi_school_class` [ RunTime:0.000604s ]
  5. SELECT * FROM `fqi_school_class` WHERE `school_id` = 6837 [ RunTime:0.000209s ]
  6. SHOW FULL COLUMNS FROM `fqi_school_campus` [ RunTime:0.000614s ]
  7. SELECT * FROM `fqi_school_campus` WHERE `school_id` = 6837 [ RunTime:0.000221s ]
  8. SHOW FULL COLUMNS FROM `fqi_school_course` [ RunTime:0.000701s ]
  9. SELECT `a`.*,`content` FROM `fqi_school_course` `a` LEFT JOIN `fqi_school_course_content` `b` ON `b`.`content_id`=`a`.`content_id` WHERE `school_id` = 6837 AND `a`.`content_id` = '94033' AND `course_status` = 1 AND `school_status` = 1 LIMIT 1 [ RunTime:0.000762s ]
  10. (select content_id,course_name from fqi_school_course where school_id = '6837' and content_id < '94033' and site_id = '22' order by content_id desc limit 1) union all(select content_id,course_name from fqi_school_course where school_id = '6837' and content_id > '94033' and site_id <= '22' order by content_id asc limit 1) [ RunTime:0.001445s ]
  11. SELECT * FROM `fqi_school_course` WHERE `school_id` = 6837 AND `site_id` = 22 AND `course_status` = 1 AND `school_status` = 1 AND `school_class_id` = 22736 ORDER BY `course_id` DESC LIMIT 4 [ RunTime:0.000369s ]
  12. SELECT * FROM `fqi_school_course` WHERE `school_id` = 6837 AND `site_id` = 22 AND `course_status` = 1 AND `school_status` = 1 ORDER BY `course_id` DESC LIMIT 10 [ RunTime:0.000287s ]
  13. SELECT COUNT(*) AS think_count FROM `fqi_school_course` WHERE `school_id` = 6837 AND `course_status` = 1 [ RunTime:0.000182s ]
  14. SHOW FULL COLUMNS FROM `fqi_school_teacher` [ RunTime:0.000717s ]
  15. SELECT COUNT(*) AS think_count FROM `fqi_school_teacher` WHERE `school_id` = '6837' [ RunTime:0.000257s ]
  16. SHOW FULL COLUMNS FROM `fqi_school_comments` [ RunTime:0.000615s ]
  17. SELECT COUNT(*) AS think_count FROM `fqi_school_comments` WHERE `school_id` = '6837' [ RunTime:0.000194s ]
  18. SELECT `content_id`,`course_name`,`a`.`school_id`,`b`.`school_name` FROM `fqi_school_course` `a` LEFT JOIN `fqi_school` `b` ON `b`.`school_id`=`a`.`school_id` WHERE `a`.`site_id` = '22' AND `b`.`school_status` = '1' AND `course_status` = 1 AND `course_id` < '94033' ORDER BY `content_id` DESC LIMIT 20 [ RunTime:0.034662s ]
0.047890s