aggregate聚合查询分组后如何获得多字段

有如下记录：

{“_id”:ObjectId(“7bc”),”user”:”阮七”,”age”:19,”class”:”初三”,”math_score”:10,”eng_score”:76}
{“_id”:ObjectId(“7bd”),”user”:”张怪”,”age”:23,”class”:”大三”,”math_score”:19,”eng_score”:12}
{“_id”:ObjectId(“7be”),”user”:”李九”,”age”:20,”class”:”大三”,”math_score”:98,”eng_score”:23}
{“_id”:ObjectId(“7bf”),”user”:”张丰”,”age”:27,”class”:”博硕”,”math_score”:12,”eng_score”:80}
{“_id”:ObjectId(“7c0″),”user”:”葫娃”,”age”:48,”class”:”成教”,”math_score”:10,”eng_score”:12}
{“_id”:ObjectId(“7c1″),”user”:”哪吒”,”age”:55,”class”:”成教”,”math_score”:96,”eng_score”:49}

1）希望按照class分组，找出math_score值最大的整条记录(文档)，如class为‘大三’的整行：
{“_id”:ObjectId(“7be”),”user”:”李九”,”age”:20,”class”:”大三”,”math_score”:98,”eng_score”:23}

2）希望按照class分组，找出 math_score+eng_score 和最小的整条记录(文档)，如class为‘大三’的整行：
{“_id”:ObjectId(“7bd”),”user”:”张怪”,”age”:23,”class”:”大三”,”math_score”:19,”eng_score”:12}

刚接触mongodb，没能自己搞出来，敬请指点！

<code class="hljs language-bash">db.stu.aggregate([
        {
            <span class="hljs-variable">$group</span>:{
                _id:<span class="hljs-string">"<span class="hljs-variable">$class</span>"</span>, 
                maxMathScore:{<span class="hljs-variable">$max</span>:<span class="hljs-string">"<span class="hljs-variable">$math_score</span>"</span>}
                //// 最大分数有了，但最大分数的学生姓名怎么搞？
            }
        }
])</code>

谢谢！